A committee is to consist of a chair, three hagglers, and four do-nothings. The committee is formed by choosing randomly from a pool of 10 people and assigning them to the various “jobs.” a. How many different committees are possible? [hinT: See Example 5.] b. Norman is eager to be the chair of the committee. What is the probability that he will get his wish? c. Norman’s girlfriend Norma is less ambitious and would be happy to hold any position on the committee provided that Norman is also selected as a committee member. What is the probability that she will get her wish and serve on the committee?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
A committee is to consist of a chair, three
hagglers, and four do-nothings. The committee is formed
by choosing randomly from a pool of 10 people and assigning
them to the various “jobs.”
a. How many different committees are possible?
[hinT: See Example
5.]
b. Norman is eager to be the chair of the committee. What
is the
c. Norman’s girlfriend Norma is less ambitious and would
be happy to hold any position on the committee provided
that Norman is also selected as a committee
member. What is the probability that she will get her
wish and serve on the committee?
d. Norma does not get along with Oona (who is also in
the pool of prospective members) and would be most
unhappy
if Oona were to chair the committee. Find the
probability that all Norma’s wishes will be fulfilled:
She and Norman are on the committee, and it is not
chaired by Oona.
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