# 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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