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Answer:
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!!!
Answer:
so noun: probability
the extent to which something is probable; the likelihood of something happening or being the case.
"the rain will make the probability of their arrival even greater"
h
Similar:
likelihood
likeliness
prospect
expectation
chance
chances
odds
possibility
a probable or the most probable event.
plural noun: probabilities
"for a time revolution was a strong probability"
h
Similar:
probable event
prospect
possibility
good/fair/reasonable bet
Mathematics
the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.
"the area under the curve represents probability"
Phrases
in all probability — used to convey that something is very likely.
"he would in all probability make himself known"
Origin
late Middle English: from Latin probabilitas, from probabilis ‘provable, credible’ (see probable).
Translate probability to
Use over time for: probability
Step-by-step explanation:
