Exercise 118 Explain in your own words what is meant by the

Exercise 11-8
Explain in your own words what is meant by the following statements. Include the long-run interpretation of probability in your answer, and relate your response to the situation’s context.
a. There is a .3 probability of rain tomorrow.
b. Your probability of winning at a daily number lottery game is 1/1000.
c. The probability that a five-card poker hand contains four of a kind is .00024.
d. The probability of getting a red M&M candy is .2.
e. The National Climatic Data Center estimates a 70% probability of having a white Christmas in Minneapolis.
f. A researcher from Ohio State University estimates that entrepreneurs who open a restaurant business have a 60% probability of failing.

Exercise 11-10
A college professor was assigned to a committee of six people, composed of four men and two women. The committee selected two officers to carry out the majority of its administrative work, and both of the women were selected. The professor wondered whether or not this constituted evidence of subtle discrimination, so she considered how unlikely such an event would be if the two officers had been chosen at random from the six committee
members.
a. Suppose the six committee members are named Alice, Bonnie, Carlos, Danny, Evan, and Frank. Describe how you might use a fair, six-sided die to simulate the random selection of two people to be officers for this committee. [Hint: Keep in mind the officers have to be different people.]
b. Use a die to carry out this simulation for a total of 50 repetitions. In how many of these 50 repetitions did the two women end up being the officers? What is your empirical estimate of that probability?
c. Calculate the mean number of men in these 50 simulated pairs of officers.

Exercise 11-11
Reconsider the previous exercise.
a. To pursue a theoretical analysis, begin by listing all possible pairs of officers that could be chosen from among these six people.
b. How many pairs are possible? How many of the pairs consist of two women?
c. What is the theoretical probability of obtaining two women officers if you randomly choose two people from among these committee members? Is this outcome impossible? Rare? Uncommon? Likely?
d. If the process of randomly selecting two people from among these six people were repeated over and over, in the long run what percentage of the time would two men be selected as officers? Would such an outcome be a surprising result using random selection?
e. Repeat part d for the outcome of one man and one woman.
f. If the two officers were chosen at random, what would be the most likely gender breakdown, two men, two women, or one of each?
g. Use the sample space in part a to calculate the theoretical expected number of men among the two officers. How close did your simulated estimate come to the theoretical expected value?

Solution

Exercise 11-8

a. There is a .3 probability of rain tomorrow.

Interpretation:

This statement means that there are 30% chances of rain tomorrow.

b. Your probability of winning at a daily number lottery game is 1/1000.

Interpretation:

This statement means that only 1 person of 1000 playing a lottery game wins, rest of the 999 people lose.

c. The probability that a five-card poker hand contains four of a kind is .00024.

Interpretation:

This statement means that a poker hand of 5 cards can have 4 cards from the same suit 24 times out of 100000.

d. The probability of getting a red M&M candy is .2.

Interpretation:

This statement means that 2 out of every 10 M&M candies are red.

e. The National Climatic Data Center estimates a 70% probability of having a white Christmas in Minneapolis.

Interpretation:

This statement means that at per National Climate Data Center estimates, 7 out of every 10 christmas are white in Minneapolis.

f. A researcher from Ohio State University estimates that entrepreneurs who open a restaurant business have a 60% probability of failing.

Interpretation:

This statement means that according to a researcher from Ohio State University, 6 out of 10 entrepreneurs who open restaurant business, do not scceed.