IfXis a random variable with expected value 2, then the expected value of 5Xwill be

7

10

2

5

A coin is tossed 6 times. The probability of heads on any toss is0.3. LetXbe the number of heads in 6 tosses. Then we have:

P(1 < X <=4) =0.579

P(1 <= X <=4) =0.579

P(1 < X <=5) =0.579

A family hasthreechildren who are 10, 15, and 18 years old. The father, trying to explain expected values to his 15 year old, decided to use the ages of his children as an example. He randomly chosetwoof the three children, and setXto be the average age of those two. Then he asked his 15 year old to find the expected value ofX. Which of the following answers would be correct? (Assume that all the possible pairs are equally likely.)

15 years

15.67 years

14.33 years

Evgenibakes a cake and invites two friends to join him in eating it. They will split the cake evenly between whoever shows up (and the cook). They know that he is an erratic baker at best, and independently each toss a coin to decide whether they will go or not. The chance that Evgenigets to eatlessthanhalf the cake is:

0.75

0.25

0.5