A player of the National Basketball Association’s Portland Trail Blazers is the best free-throw shooter on the team, making 94% of his shots. Assume that late in a basketball game, the player is fouled and is awarded two shots. a. What is the probability that he will make both shots? (to 4 declmals) b. What s the prabability that he will make at least one shct? (to 4 declmals) c. What is the probability that he will miss both shots? (to 4 decimals) int d. Late in a basketball game, a team aften intent onally fouls an apposing player in arder to stop the game clack. The usual strategy is to intentionally foul the other team's worst free-throw shooter Assume that the Partland Trail Blazers' cenber makes 56% of his free-throw shots. Calcuiate the probe ities for the center ad shown in perts a b) and c and show that intentionally fouling the Porte d Trail Blazers center is e er strategy then intentionally fouling Jamal Cr wford. Assu e as in parts(a) b) and e that two shots I be。О ed What is the probabiity that Portland Trail Blazers' center will make both shots? he Portiland Try is (to 4 declmals) What is the probabiity that Portland Trail Blazers' center will make at least one shat? (to 4 declmals) What is the probabiity that Portland Trail Blazers' center will miss both shots? (to 4 decimals)

The data for the probabilities are shown in the table below.

- A represents the probability of making the two shots for each of the best and worst shooter on the Portland Trail Blazers' team

- B represents the probability of making at least one shot for each of the best and worst shooter on the Portland Trail Blazers' team.

- C represents the probability of not making any of the two shots for each of the best and worst shooter on the Portland Trail Blazers' team.

N | Best ||| Worst

A | 0.8836 | 0.3136

B | 0.9964 | 0.8064

C | 0.0036 | 0.1936

It becomes evident why fouling the worst shooter on the team is a better tactic. The probabilities of the best shooter making the basket over the range of those two free shots are way better than the chances for the worst shooter.

Step-by-step explanation:

Part 1

Probability of the best shooter of the National Basketball Association’s Portland Trail Blazers making a shot = P(B) = 94% = 0.94

Probability that he doesn't make a shot = P(B') = 1 - 0.94 = 0.06

a) Probability that the best shooter on the team makes the two shots awarded = P(B) × P(B) = 0.94 × 0.94 = 0.8836

b) Probability that the best shooter on the team makes at least one shot.

This is a sum of probabilities that he makes only one shot and that he makes two shots.

Probability that he makes only one shot

= P(B) × P(B') + P(B') + P(B)

= (0.94 × 0.06) + (0.06 × 0.94) = 0.1128

Probability that he makes two shots = 0.8836 (already calculated in part a)

Probability that he makes at least one shot = 0.1128 + 0.8836 = 0.9964

c) Probability that the best shooter on the team makes none of the two shots = P(B') × P(B') = 0.06 × 0.06 = 0.0036

d) If the worst shooter on the team, whose success rate is 56% is now fouled to take the two shots.

Probability of the worst shooter on the team making a shot = P(W) = 56% = 0.56

Probability that the worst shooter on the team misses a shot = P(W') = 1 - 0.56 = 0.44

Part 2

a) Probability that the worst shooter on the team makes the two shots = P(W) × P(W)

= 0.56 × 0.56 = 0.3136

b) Probability that the worst shooter on the team makes at least one shot.

This is a sum of probabilities that he makes only one shot and that he makes two shots.

Probability that he makes only one shot

= P(W) × P(W') + P(W') + P(W)

= (0.56 × 0.44) + (0.44 × 0.56) = 0.4928

Probability that he makes two shots = 0.3136 (already calculated in part a)

Probability that he makes at least one shot = 0.4928 + 0.3136 = 0.8064

c) Probability that the worst shooter makes none of the two shots = P(W') × P(W') = 0.06 × 0.06 = 0.1936

From the probabilities obtained

N | Best ||| Worst

A | 0.8836 | 0.3136

B | 0.9964 | 0.8064

C | 0.0036 | 0.1936

It becomes evident why fouling the worst shooter on the team is a better tactic. The probabilities of the best shooter making the basket over the range of those two free shots are way better than the chances for the worst shooter.

Hope this Helps!!!

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