Question

Suppose a basketball player has made 305 out of 372 free throws. If the player makes the next 2 free throws, I will pay you $5. Otherwise you pay me $10. Step 2 of 2 : If you played this game 626 times how much would you expect to win or lose? Round your answer to two decimal places. Losses must be entered as negative.

Answer 1

a. -$0.145

b. -$10

Explanation:

Given:

Total Possible Throws = 372

Number of throws = 305

Let P(T) = Probability that the player makes the next throw

P(T) = 305/372

Probability that the player makes the next two throws is then given by:

Probability that he makes the next throw and he also makes the next throw.

= P(T) and P(T)

= P(T) * P(T)

= 305/372 * 305/372

= (305/372)²

= 0.672223667476008

= 0.672 -- Approximated

Let P(T') = Probability the the player doesn't make the next two throws

P(T') = 1 - P(T)

P(T') = 1 - 0.672

P(T') = 0.328

The expected gain for the player turns is given by:

(Probability of making both throws) * $5 + (Probability of NOT making both throws) x (-$10)

=0.627 * $5 + 0.328 * $10

= $3.135 - $3.28

= -$0.145

b.

Probability that he makes the next 626 throws

= P(T)^626

= (305/372)^626

= 1.027588097043E−54

Let P(T') = Probability the the player doesn't make the next two throws

P(T') = 1 - P(T)

P(T') = 1 - 1.027588097043E−54

P(T') = 1

The expected gain for the player turns is given by:

(Probability of making all 626 throws) * $5 + (Probability of NOT making all 626 throws) x (-$10)

=1.027588097043E−54 * $5 + 1 * -$10

= =1.027588097043E−54 * $5 - $10

= -$9.999999

= -$10