# A company is to hire two new employees. They have prepared a final list of eight candidates, all of whom are equally qualified. Of these eight candidates, five are women. Suppose the company decides to select two persons randomly from these eight candidates. a. What is the probability that: i. Both candidate selected are women? ii. At least one candidate selected is a woman? iii. Second candidate is a woman.

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.

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Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.

A company is to hire two new employees. They have prepared a final list of eight candidates, all

of whom are equally qualified. Of these eight candidates, five are women. Suppose the

company decides to select two persons randomly from these eight candidates.

a. What is the probability that:

i. Both candidate selected are women?

ii. At least one candidate selected is a woman?

iii. Second candidate is a woman.

iv. First candidate is a woman given that the second candidate is a woman.

b. Let X denote the number of women in this sample.

i. Write the probability distribution of X.

ii. Find the standard deviation of X.

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