The biathlete hits the target with a probability of 0.8, he shoots 5 times, find the probability that he will miss all five times.
July 25, 2021 | education
| The probability of not hitting the target all five times is equal to the product of the probabilities of not hitting the target for each of the shots:
P = P1 × P2 × P3 × P4 × P5.
1) Find the probability of not hitting the target on the first shot:
P1 = 1 – 0.8 = 0.2.
2) The probability of not hitting the target is the same for each shot:
P1 = P2 = P3 = P4 = P5 = 0.2.
3) Find the probability of not hitting the target all 5 times:
P = 0.2 x 0.2 x 0.2 x 0.2 x 0.2 = 0.00032.
0.00032 × 100% = 0.032%.
Answer: the probability of not hitting the target all 5 times is 0.00032 (0.032%).
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