Leadership Skills
Leadership quality incorporates many of the diverse skills and the qualities, and for many of the people it does not come naturally. Good leader is a one who can find balance in managing, disciplining, delegating, instructing , encouraging, and sympathizing. Good leader do strives to accomplish the goal common among most of the leaders: to make the people believe in your vision, make them follow you, and do whatever it do takes to get a job done.
As the manager/leader, all the eyes are on you. You will be representing the company; do choose your words carefully, be confident leader, and do make your presence known without being haughty or condescending. No person wants to feel like as if they are at a bottom of totem pole, so as the leader, do relate to your employees, try to be on their level, and do set examples. The people like to emulate the leaders, and if you are conscious of all your actions, the people will follow your lead and will strive to reach the top. All the parties will profit.
Since the leadership is not inherent in most of the people, a wise leader must work with others to help them out to develop their own leadership skills and the style; education is the key factor to the successful leadership. It is not easy task to get everyone to work together amicably for good of the common goal, but this can be done. Good leader do sets a tone for each and every project and will helps to motivate a team to do the best it can do. Good leader also know to give credit to people who have done good job.

Leadership Qualities A leader should have:

Vision of where he/she is going.
Ability to do communicate well to the his/her followers.
The shepherd’s heart for his/her people who work under.
Understanding of a role of management as it will relates to the leadership.
Deep desire to go on learning new things.
Resolve to handle pain which comes with the leadership.
Anointing of Spirit of the God in his/her life.

Leadership Skill

Ten Skills of Leadership

Getting and Giving the Information is probably important competency required of the leaders.

If you cannot communicate effectively, then none other leadership skill will do compensate for this lack. First and the foremost thing is, you should be able to exchange the information effectively and accurately.
Understanding the Group Needs and Characteristics It is very essential that we do first understand ourselves and our own needs and the characteristics. Only then we can know and understand the other people's needs and characters. This understanding will hopefully come naturally as we mature, creeping over us like a ivy winding about the tree. By directly exploring and encouraging the discovery of these kinds of personality traits, we can do accelerate maturing of the leader, adding the fertilizer to ivy and the tree. About Understanding the Group Needs and the Characteristics
Knowing and Understanding the Group Resources
Recognize the knowledge and the use of the group resources as the major technique in bringing the group together and creating a commitment to the common goals.
Recognize that the resources are theoretically limitless, and that the leader's and the group's the ability to recognize and utilized the diverse resources tremendously affects what a group can accomplish.
Involve more and more people in active leadership by giving each of them a part according to his or her resources.
Evaluate a impact availability of the resources has on doing the job and maintaining a group.
Controlling a Group
Recognize how his own behavior will influences and can control others.
Distinguish between the controlling group performance and setting an example.
Identify the control as the function of group, or of the facilitator, and advantages and disadvantages of each having this responsibility.
Identify the different techniques for controlling the group performance and the suitability in a different situations.
Deploy the group resources to best interests of a group while encouraging the personal growth.
Evaluate the leadership performance in terms of the group performance.
Counseling
Counseling is the private talk with someone which helps the individual to solve a personal problem. As a leader, people will do come to you with the problems. Because you are the leader, you will spot the people with problems. You cannot turn them away or will just let them suffer, because a ignored problem, if serious, almost inevitably will become a group problem. Counseling is been considered pretty difficult. The professional counselors, like the vocational counselors, clergymen, lawyers, bankers, teachers, psychiatrists and others, sometimes you will spend years learning how to counsel in their fields. People often will pay large amount of money to be counseled.
Setting an ExampleSetting an Example is the personal behavior independent of any external influences. While very simple competency on its face, none is more important. Fail to demonstrate this competency to the members of your group, and you will be doomed to the negative results. No matter how good the line you talk, if you do not match it with your behavior, you will not get any respect and will find it increasingly difficult to get a group to work with you. It might be more difficult under some of the circumstances to set the positive example, but that will not stop you! Setting an Example is where your backbone will show. If you have the character, if your character has the integrity--that is, if who you are on outside is been lined up with who you are on inside--you will accomplish a far more than you may imagine possible. For this kind of the leader, as long as he do takes care of all his follower's needs, enjoys respect, loyalty, and love.
Representing a GroupRepresenting Group is accurately communicating to the non-group members a sum of the group members ideas, feelings, etc., and vice versa. A leader should represent his team on the great variety of the issues. Some of these issues and a need for the decision representing a group interests will be known well in advance; and others will not be. Under any of the circumstances, to faithfully represent a group, you should:
Fully understand nature of the problem.
Know how a decision was been reached and be able to communicate this to others.
Accurately and responsibly do communicate from and back to a original group.
Realize that the other groups might derive their entire picture of the other group through you, the representative. You should be consistent, possess the integrity, and be fair to all the parties.
Problem-Solving
Effective use of the problem-solving will do more than any other competency to advance both getting a job done and keeping a group together. It is the "umbrella" competency in all its effect on the variety of issues. The problem-solving is useful both in the group situations and in the one-on-one.
EvaluationEvaluation attitude is the predisposition to continually examine and analyze all our efforts. Evaluation is very critical component of cyclical learning process. It will not occur just formally at conclusion of the activities, but also informally as well, by all been involved, throughout a project or task. An Evaluation Attitude is one of the principals which form a basis of White Stag Leadership Development Program. One who will apply this attitude or the technique will be aware continually of the objectives of his learning's and will do attempt to measure his growth towards them.
Sharing the LeadershipSharing a Leadership translates on one level into the "styles" of the leadership. Depending upon the job and a group, certain ways for a leader to work with a group will be more appropriate than the others. It will also identifies some generic roles groups have which can be distributed among all the members. Sharing the leadership is a key function of the leader. Ability to extend herself, to accomplish the jobs greater than a person alone can handle, is one of a key elements of the society's success today. Never has the society been so productive

Probability

Three Different Concepts of Probability
The classical interpretation of probability is a theoretical probability based on the physics of the experiment, but does not require the experiment to be performed. For example, we know that the probability of a balanced coin turning up heads is equal to 0.5 without ever performing trials of the experiment. Under the classical interpretation, the probability of an event is defined as the ratio of the number of outcomes favorable to the event divided by the total number of possible outcomes.
Sometimes a situation may be too complex to understand the physical nature of it well enough to calculate probabilities. However, by running a large number of trials and observing the outcomes, we can estimate the probability. This is the empirical probability based on long-run relative frequencies and is defined as the ratio of the number of observed outcomes favorable to the event divided by the total number of observed outcomes. The larger the number of trials, the more accurate the estimate of probability. If the system can be modeled by computer, then simulations can be performed in place of physical trials.
A manager frequently faces situations in which neither classical nor empirical probabilities are useful. For example, in a one-shot situation such as the launch of a unique product, the probability of success can neither be calculated nor estimated from repeated trials. However, the manager may make an educated guess of the probability. This subjective probability can be thought of as a person's degree of confidence that the event will occur. In absence of better information upon which to rely, subjective probability may be used to make logically consistent decisions, but the quality of those decisions depends on the accuracy of the subjective estimate.

Outcomes and Events
An event is a subset of all of the possible outcomes of an experiment. For example, if an experiment consists of flipping a coin two times, the possible outcomes are: heads, heads heads, tails tails, heads tails, tails One can define the showing of heads at least one time to be an event, and this event would consist of three of the four possible outcomes.
Given that the probability of each outcome is known, the probability of an event can be determined by summing the probabilities of the individual outcomes associated with the event.
A composite event is an event defined by the union or intersection of two events. The union of two events is expressed by the "or" function. For example, the probability that either Event A or Event B (or both) will occur is expressed by P(A or B). The intersection of two events is the probability that both events will occur and is expressed by the "and" function. For exampe, the probability that both Event A and Event B will occur is expressed by P(A and B).
Law of Addition
Consider the following Venn diagram in which each of the 25 dots represents an outcome and each of the two circles represents an event.

In the above diagram, Event A is considered to have occurred if an experiment's outcome, represented by one of the dots, falls within the bounds of the left circle. Similarly, Event B is considered to have occurred if an experiment's outcome falls within the bounds of the right circle. If the outcome falls within the overlapping region of the two circles, then both Event A and Event B are considered to have occurred.
There are 5 outcomes that fall in the definition of Event A and 6 outcomes that fall in the definition of Event B. Assuming that each outcome represented by a dot occurs with equal probability, the probability if Event A is 5/25 or 1/5, and the probability of Event B is 6/25. The probability of Event A or Event B would be the total number of outcomes in the orange area divided by the total number of possible outcomes. The probability of Event A or Event B then is 9/25.
Note that this result is not simply the sum of the probabilities of each event, which would be equal to 11/25. Since there are two outcomes in the overlapping area, these outcomes are counted twice if we simply sum the probabilities of the two events. To prevent this double counting of the outcomes common to both events, we need to subtract the probability of those two outcomes so that they are counted only once. The result is the law of addition, which states that the probability of Event A or Event B (or both) occurring is given by:
P(A or B) = P(A) + P(B) - P(A and B)
This addition rule is useful for determining the probability that at least one event will occur. Note that for mutually exclusive events there is no overlap of the two events so:
P(A and B) = 0
and the law of addition reduces to:
P(A or B) = P(A) + P(B)

Conditional Probability
Sometimes it is useful to know the probability that an event will occur given that another event occurred. Given two possible events, if we know that one event occurred we can apply this information in calculating the other event's probability. Consider the Venn diagram of the previous section with the two overlapping circles. If we know that Event B occurred, then the effective sample space is reduced to those outcomes associated with Event B, and the Venn diagram can be simplified as shown:

The probability that Event A also has occurred is the probability of Events A and B relative to the probability of Event B. Assuming equal probability outcomes, given two outcomes in the overlapping area and six outcomes in B, the probability that Event A occurred would be 2/6. More generally, P(A given B) = P(A and B) ---------------------------- P(B)

Law of Multiplication
The probability of both events occurring can be calculated by rearranging the terms in the expression of conditional probability. Solving for P(A and B), we get:
P(A and B) = P(A given B) x P(B)
For independent events, the probability of Event A is not affected by the occurance of Event B, so P(A given B) = P(A), and
P(A and B) = P(A) x P(B)