The probability of hitting the target by the first shooter is 0.9, the second – 0.7. Both shooters fired one shot.

The probability of hitting the target by the first shooter is 0.9, the second – 0.7. Both shooters fired one shot. What is the probability that the target is hit: a) at least once; b) two times; c) once?

The probability that the target is hit for the first shooter: p = 0.9;
The probability of a miss for him: q = 1 – p = 1 – 0.9 = 0.1.
The probability that the target is hit for the second shooter: p = 0.7;
The probability of a miss for him: q = 1 – p = 1 – 0.7 = 0.3.
a) Probability that both shooters miss:
P2 (0) = q1 q2 = 0.1 0.3 = 0.03.
The probability that the target is hit at least once:
P2 (> 0) = 1 – P2 (0) = 1 – 0.03 = 0.97.
b) The probability that the target is hit 2 times:
P2 (2) = p1 p2 = 0.9 0.7 = 0.63.
c) The probability that the target is hit 1 time
P2 (1) = p1 q2 + q1 p2 = 0.9 0.3 + 0.1 0.7 = 0.27 + 0.07 = 0.34.
Answer: a) 0.97; b) 0.63; c) 0.34.