Question

If you win $100 for rolling a 12, win $10 for rolling a number less than 6, and lose $4 for rolling anything else, what are your expected winnings per play?

a. $1.94         b. $4.72         c. $2.78         d. -$.68

A committee of 7 is be selected from a group of 22 people. How many such committees are possible?

a. 22,254      b. 319,770      c, 170,544     d. 101,458

A woman plans on having four children. What is the probability she will have at most 2 boys?

a. 11/16         b. 1/2         c. 9/16        d. 6/16

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%

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)          

Answer 1

A.

X	100	10	-4
P(X)	1/36	10/36	25/36

The probability of obtaining a sum of 12 is 1/36.

The probability of obtaining a sum of less than 6 is 10/36.

The probability of obtaining anything else is 25/36.

The expected winnings per play is $ 2.78.

E(X) = 100*(1/36)+ 10*(10/36)- 4*(25/36) = 2.777778 ~ $ 2.78

C option is the correct answer.

B.

A committee of 7 is to be selected from a group of 22 people.

It can be done in

C option is the correct answer.

C.

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.

D option is the correct answer.

D.

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 option is the correct answer.