Question

Suppose a basketball player has made 223223 out of 406406 free throws. If the player makes the next 22 free throws, I will pay you $20$ 20. Otherwise you pay me $8$ 8. Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Answer 1

Expected value E = $0.45

Explanation:

Expected value E = P×w - P'×l

Where;

P = probability of making the next 2 throw.

P = 223/406 × 223/406 = 0.3017

P' = probability of not making a throw.

P' = 1 - P = 1 - 0.3017

P' = 0.6983

w = expected win = $20

l = Expected loss = $8

Substituting the values;

E = 0.3017 × $20 - 0.6983 × $8

E = $0.4476

Expected value E = $0.45