Final answer:
The probability that the target is hit by at least one of the two airplanes is 0.44. This is calculated by adding the probability of the first plane hitting (0.3) to the probability of the first plane missing and the second plane hitting (0.7 × 0.2 = 0.14).
Step-by-step explanation:
The problem is about calculating the probability that a target is hit by at least one of two airplanes bombing in succession, where the second airplane bombs only if the first one misses. The probability of the first airplane hitting is given as 0.3, and the probability of the second airplane hitting is 0.2.
To find the overall probability of hitting the target, we need to consider two scenarios: the first airplane hits the target, or the first airplane misses but the second airplane hits.
The probability that the first airplane hits the target is directly given as 0.3. The probability that the first airplane misses is 1 - 0.3 = 0.7. Since the second airplane will bomb only if the first one misses, we multiply the probability that the first airplane misses with the probability that the second airplane hits, i.e., 0.7 × 0.2 = 0.14.
The combined probability that the target is hit by either the first or the second airplane can be found through the formula P(A OR B) = P(A) + P(B) − P(A AND B). However, since the second airplane bombs only if the first misses, there is no overlap in the events, which means the formula simplifies to P(A OR B) = P(A) + P(B). Thus, the total probability that the target is hit is given by 0.3 + 0.14 = 0.44.