Question

Probability and Statistics
Could you please solve the following questions with specifying the answers

A. Thirty-nine percent of the houses in a certain neighborhood read the New Yorker, 43 percent read the Philadelphia Inquirer, and 9 percent read both. What percent read at least one of these publications?

a. 64%        b. 79%         c. 82%            d. 73%

B. What is the probability of getting at least one 10 in twenty rolls of a pair of dice?

a. (33/36)²⁰         b. 1-(3/36)²⁰        c.  1- (33/36)²⁰       d. 1-20(33/36)           

C. A certain US Senator is a devoted family man and lives modestly. Given these facts, which is more likely

a. He took a bribe from a lobbyist  

b. He took a bribe from a lobbyist and used it to pay for his daughter’s medical needs.

c. equally likely   

Answer 1

A.

P(read the New Yorker) = 0.39

P(read the Philadelphia Inquirer) = 0.43

P( read both the publications) = 0.09

P(read at least these publications) =??

Using the formula, P(AUB) = P(A) + P(B) - P(A B)

P(read at least these publications)

= P(read the New Yorker) + P(read the Philadelphia Inquirer) - P( read both the publications)

= 0.39 + 0.43 - 0.09 = 0.73

73% read at least these publications.

B.

The probability of obtaining a 10 is 3/36.

Now out of 20 rolls, we need to find the probability of getting at least one 10 in twenty rolls of a pair of dice.

P(X 1) = 1 - P(X<1) = 1 - P(X = 0) = 1 - P(None) =

= 0.8245195

C.

A certain US Senator is a devoted family man and lives modestly.

The answer is he took a bribe from a lobbyist and used it to pay for his daughter’s medical needs.