The probability of each missile hitting the target is 0.6; individual missile hits are independent.

The probability of each missile hitting the target is 0.6; individual missile hits are independent. Each missile that hits hits the target with a probability of 0.8. Shooting is conducted until the target is hit or until all ammunition is consumed. The base has ammunition for 6 missiles. Find the probability that not all of the ammunition will be used up.

1. The probability of hitting the target with each missile:

v1 = 0.6 * 0.8 = 0.48.

2. The likelihood that the target will not be hit by each missile:

u1 = 1 – v1 = 1 – 0.48 = 0.52.

3. Since the hits of individual missiles are independent, the probability that after launching n missiles the target will not be hit is determined by the formula:

un = u1 ^ n,

and for n = 5 we get:

u5 = u1 ^ 5 = 0.52 ^ 5.

4. Thus, for the probability of hitting a target with one of the first five missiles launched, we get:

v5 = 1 – u5;
v5 = 1 – 0.52 ^ 5 ≈ 1 – 0.038 = 0.962.
Answer: 0.962.