The shooter shoots at targets three times. The probability of hitting a target with one shot is 0.6

The shooter shoots at targets three times. The probability of hitting a target with one shot is 0.6. Find the probability that the shooter hits the targets the first time and misses the last two.

Let hitting the target be event A.
A slip, let it be an event V.
The hit probability is given in the condition.
Let’s calculate the probability of a miss:
P (B) = 1 – P (A);
P (B) = 1 – 0.6;
P (B) = 0.4;
Consider an ABB event – one hit and two misses.
Misses and hits in each shot are independent of the results of other shots.
Let’s find the probability of the event ABB.
P (ABB) = P (A) ∙ P (B) ∙ P (B);
P (ABB) = P (A) ∙ [1 – P (A)] ∙ [1 – P (A)];
P (ABB) = 0.6 ∙ 0.4 ∙ 0.4;
P (ABB) = 0.096;
Answer: The probability that the shooter hits the targets for the first time and misses the last two is 0.096.