Question

A coin has an equal probability of coming up heads or tails when tossed. Suppose a game is played where a player is awarded 10 points if a pair of tosses both come up heads, 8 points if they both come up tails, and 2 points if the result is 1 head and 1 tail.

What is the expected value of the score for a pair of tosses?
A)6.3
B)5.9
C)5.5
D)6.7

Answer 1

C) 5.5

Explanation:

The expected value is the sum of products of points and the probability of obtaining those points.

The probabilities are ...

P(HH) = 1/4

P(HT or TH) = 1/4 +1/4 = 1/2

P(TT) = 1/4

Then the expected value of the score is the sum of ...

10×P(HH) = 10/4 = 2.5

8×P(TT) = 8/4 = 2.0

2×P(HT or TH) = 2/2 = 1.0

The expected score is 2.5+2.0+1.0 = 5.5.