To solve this problem, we need to find the probability that the aircraft will be brought down by at least one of the four shots.
Step 1: Understand the problem
The anti-aircraft gun fires four shots at a time. The probabilities of the first, second, third, and fourth shot hitting the enemy aircraft are given as:
Probability of first shot hitting = 0.7
Probability of second shot hitting = 0.6
Probability of third shot hitting = 0.5
Probability of fourth shot hitting = 0.4
We need to find the probability that at least one shot hits the aircraft.
Step 2: Calculate the probability that no shot hits the target
The probability that a shot misses is the complement of the probability that it hits:
Probability of first shot missing = 1 - 0.7 = 0.3
Probability of second shot missing = 1 - 0.6 = 0.4
Probability of third shot missing = 1 - 0.5 = 0.5
Probability of fourth shot missing = 1 - 0.4 = 0.6
Now, to find the probability that all four shots miss, we multiply the probabilities of missing:
Probability that all shots miss = 0.3 * 0.4 * 0.5 * 0.6 = 0.036
Step 3: Calculate the probability that at least one shot hits
The probability that at least one shot hits is the complement of the probability that all shots miss:
Probability that at least one shot hits = 1 - Probability that all shots miss
Probability that at least one shot hits = 1 - 0.036 = 0.964
Step 4: Conclusion
The probability that the four shots will bring the aircraft down is 0.964.
Thus, the correct answer is 4. 0.964.
