1. The percentage of American men who say they would marry the same woman if they had to do it all over again is 80%. The percentage of American women who say they would marry the same man again is 50% (Source: Harper's Index).

a. In a group of 10 married men, what is the probability that:

i. At least 7 will claim that they would marry the same woman again? (10 points)

ii. Less than 4 will say this? (10 points)

b. In a group of 10 married women, what is the probability that:

i. At least 7 will claim that they would marry the same man again? (10 points)

ii. Less than 4 will say this? (10 points)

c. In a group of 20 married men, what is the expected number of men that will claim they would marry the same woman again? (5 points)

d. In a group of 20 married women, what is the expected number of women that will claim they would marry the same man again? (5 points)

2. Richard has just been given a 10-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Richard doesn't know any of the answers because he has not attended class recently. Assuming that Richard guesses on all 10 questions, find the following probabilities:

a. What is the probability that he will answer all questions correctly? (10 points)

b. What is the probability that he will answer all questions incorrectly? (10 points)

c. What is the probability that he will answer at least 7 questions correctly? (10 points)

d. What is the probability that he will answer at most 6 questions correctly? (10 points)

e. What is the expected number of questions that he will answer correctly? (10 points)