Question

During the NCAA basketball tournament season, affectionately called March Madness part of one team's strategy is to fou their opponent. If his free-throw shooting percentage is lower than this two-point field goal percentage Drake's free-throw shooting percentage is lower and is only 52.7% After being fouled he gets two free-throw shots each worth one point. Calculate the expected value of the number of points

Answer 1

1.054points

Step-by-step explanation:

The expected value can be calculated as the sum of each possible point multiplied by it probability. So, we first need to calculate the following probabilities.

Probability to get 0 points: He gets 0 points if he fail both throw shots, so the probability is

P(0) = (1 - 0.527)(1 - 0.527) = (0.473)(0.473) = 0.2237

Because the probability to fail is 1 - 0.527 = 0.473.

Probability to get 2 points: We can calculate this probability as

p(2) = (0.527)(0.527) = 0.2777

Probability to get 1 point: This probability is the complement of the others, so

P(1) = 1 - 0.2237 - 0.2777 = 0.4986

Then, we can calculate the expected value of the points as

E = 0*0.2237 + 1*0.4986 + 2*0.2777

E = 0.4986 + 0.5554

E = 1.054

Therefore, the expected value is 1.054 points