Question

Два стрелка делают по одному выстрелу по мишени. Вероятность попадания в цель 1 стрелком 0,5 вторым 0,7. Найдите вероятность того, что: а) оба промахнутся. б) оба попадут в мишень в) попадет только один г) попадет хотя бы один

Answer 1

                      попадание   промах
I стрелок             0,5               0,5
II стрелок            0,7               0,3
а) оба промахнутся  0,5*0,3 = 0,15
б) оба попадут           0,5*0,7 = 0,35 
в) 1 попадёт               0,5*0,3 + 0,7*0,5 = 0,15 + 0,35 = 0,5
г) 

Answer 2

Probability Calculations for Shooting Scenario

To calculate the probabilities, we can use the following information: - The probability of hitting the target for the first shooter is 0.5, and for the second shooter is 0.7.

a) Probability that Both Miss the Target

The probability that both shooters miss the target can be calculated using the complement rule. The complement of hitting the target is missing the target.

The probability that both miss the target is calculated as: $$ P(\text{both miss}) = (1 - 0.5) \times (1 - 0.7) = 0.5 \times 0.3 = 0.15 $$

b) Probability that Both Hit the Target

The probability that both shooters hit the target is the product of their individual probabilities of hitting the target.

The probability that both hit the target is calculated as: $$ P(\text{both hit}) = 0.5 \times 0.7 = 0.35 $$

c) Probability that Only One Hits the Target

The probability that only one shooter hits the target can be calculated by adding the probabilities of the first shooter hitting and the second shooter missing, and the first shooter missing and the second shooter hitting.

The probability that only one hits the target is calculated as: $$ P(\text{only one hits}) = (0.5 \times 0.3) + (0.5 \times 0.7) = 0.15 + 0.35 = 0.5 $$

d) Probability that At Least One Hits the Target

The probability that at least one shooter hits the target is the complement of both missing the target.

The probability that at least one hits the target is calculated as: $$ P(\text{at least one hits}) = 1 - P(\text{both miss}) = 1 - 0.15 = 0.85 $$

These are the probabilities for the given shooting scenario.