Answer on Question#38988 - Math - Statistics and Probability
Question: In a game you flip a coin twice, and record the number of heads that occur. You get 10
points for 2 heads, zero points for 1 head, and 5 points for no heads. What is the expected value
for the number of points you’ll win per turn?
Solution:
P(2 heads) = P(first flip = head)*P(second flip = head) = (1/2)(1/2) = 1/4.
P(1 head) = P(first flip = head)*P(second flip = tail) + P(first flip = tail)*P(second flip = head) = 1/4 +
1/4 = 1/2.
P(no heads) = P(first flip = tail)*P(second flip = tail) = 1/4.
event
2 heads
1 head
no heads
probability 1/4
1/2
1/4
winning
10
0
5
E(winning) = 10*P(winning = 10) + 0*P(winning = 0) + 5*P(winning = 5) = 10*(1/4) + 0*(1/2) +
5*(1/4) = 15/4.
Answer: 15/4.