Answer to Question #385 in Statistics and Probability for Keita

Question

The probability of hitting the target is 1/5. A shooter makes 10 shots. What is the probability of hitting the target at least twice?

Answer 1

The probability of missing the target is 1 – 1/5 = 4/5. Hitting the target at least twice means preventing one of the following options: hit 0 times and miss 10 times or hit 1 time and miss 9 times, and such an outcome might occur in 10 different ways (caught at the first shot or at the second, or at the third, ..., or at the 10th). Thus, the probability of hitting the target at least twice is: P = 1 – (1/5)^0·(4/5)^10 – 10*(1/5)^1·(4/5)^9 ≈ 0.624.