Question

Zared plays basketball on his high school team. One of the things he needs to practice is his free throws. On his first shot, there is a probability of 0.6 that he will make the basket. If he makes a basket, his confidence grows and the probability he makes the next shot increases by 0.05. If he misses the shot, the probability he makes the next one decreases by 0.05. He takes 5 shots. What is the probability he makes at least 3 shots?

Please answer with a tree diagram and all the outcomes. As simple and clear as possible please

Answer 1

solution:

Combination Shot P1 P2 P3 P4 P5 P 1 123 0.6 0.65 0.65 0.4 0.35 0.03549 2 124 0.6 0.65 0.4 0.35 0.6 0.03276 3 125 0.6 0.65 0.4 0.35 0.6 0.03276 4 134 0.6 0.65 0.4 0.35 0.6 0.03276 5 135 0.6 0.65 0.4 0.35 0.6 0.03276 6 145 0.6 0.4 0.35 0.6 0.65 0.03276 7 234 0.6 0.65 0.4 0.35 0.6 0.03276 8 235 0.6 0.65 0.4 0.35 0.6 0.03276 9 245 0.6 0.4 0.35 0.6 0.65 0.03276 10 345 0.6 0.4 0.35 0.6 0.65 0.03276 Total 0.33033

Combination Shot P1 P2 P3 P4 P5 P 1 1234 0.6 0.65 0.65 0.65 0.35 0.057671 2 1235 0.6 0.65 0.65 0.35 0.6 0.053235 3 1245 0.6 0.65 0.65 0.35 0.6 0.053235 4 1345 0.6 0.65 0.65 0.35 0.6 0.053235 5 2345 0.6 0.65 0.65 0.35 0.6 0.053235 0.270611

12345

0.6

0.65

0.65

0.65

0.65

0.107104

the probability he makes at least 3 shots is 0.7080

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