Question

Три стрелка стреляют по мишени . Вероятность попадания каждого из стрелков равна p1=0,3 ; p2=0,4; p3=0,7. Какова вероятность того что попадут более чем два стрелка?

Answer 1

0,084 - шанс того что все попадут

Answer 2

Problem Statement

Три стрелка стреляют по мишени. Вероятность попадания каждого из стрелков равна p1=0,3; p2=0,4; p3=0,7. Какова вероятность того, что попадут более чем два стрелка?

Solution

To find the probability that more than two arrows hit the target, we need to calculate the probability of three arrows hitting the target and the probability of exactly two arrows hitting the target, and then add them together.

Let's calculate the probability of three arrows hitting the target first. We can use the formula P1 = p1 * p2 * p3, where p1, p2, and p3 are the probabilities of each arrow hitting the target.

Using the given probabilities, we have p1 = 0.3, p2 = 0.4, and p3 = 0.7. Plugging these values into the formula, we get:

P1 = 0.3 * 0.4 * 0.7 = 0.084

Next, let's calculate the probability of exactly two arrows hitting the target. We can use the formula P2 = p1 * p2 * q3 + p1 * q2 * p3 + q1 * p2 * p3, where q1, q2, and q3 are the probabilities of each arrow missing the target (1 - p1, 1 - p2, and 1 - p3, respectively).

Using the given probabilities, we have q1 = 1 - p1 = 1 - 0.3 = 0.7, q2 = 1 - p2 = 1 - 0.4 = 0.6, and q3 = 1 - p3 = 1 - 0.7 = 0.3. Plugging these values into the formula, we get:

P2 = (0.3 * 0.4 * 0.3) + (0.3 * 0.6 * 0.7) + (0.7 * 0.4 * 0.7) = 0.036 + 0.126 + 0.196 = 0.358

Finally, we can calculate the probability of more than two arrows hitting the target by adding P1 and P2:

P = P1 + P2 = 0.084 + 0.358 = 0.442

Therefore, the probability that more than two arrows hit the target is 0.442.