# Two arrows make one shot. The probability of hitting a target with the first shooter is 0.8, and the second is 0.7

Two arrows make one shot. The probability of hitting a target with the first shooter is 0.8, and the second is 0.7. Find the probabilities of hitting the target with both arrows and hitting the target with at least one shooter

Let event A – hit the target with the first shooter, B – the second. Then event C, which consists in simultaneously hitting a target with both arrows, is a product of events A and B (C = A · B). These events occur independently of each other.
Therefore, the probability of their product is determined by the formula
P (A · B) = P (A) · P (B) and is equal to P (C) = P (A · B) = 0.7 · 0.8 = 0.56.
We now consider the event D – the defeat of the target by at least one shooter. It consists in hitting the target with either the first, the second, or both together. This event is the sum of the initiating events, i.e., D = A + B. Events A and B are joint, because they can occur in the same test. Therefore, you should use the formula P (A + B) = P (A) + P (B) -P (A · B).
We get P (D) = P (A + B) = 0.7 + 0.8–0.7 · 0.8 = 0.94.

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