# 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.

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%).

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.