The probability of hitting the target with each shot is 0.6. three hits are enough to get

The probability of hitting the target with each shot is 0.6. three hits are enough to get credit. Find the probability of getting a shooting rating if 5 shots are fired?

p = 0.6 – hit probability with one shot;
q = 1 – p = 1 – 0.6 = 0.4 is the probability of a shooter miss;
n = 5 is the number of test shots;
m = 3 is the minimum number of hits.

To pass the test, the shooter must hit the target 3, 4 or 5 times.

Let’s find the probability that the shooter will hit 3 times:
For calculations, we use the Bernoulli formula:
C (3; 5) = 5! / ((5 – 3)! * 3!) = 5! / (2! * 3!) = 5 * 4/2 = 10.
P (3; 5) = 10 * 0.6 ^ 3 * 0.4 ^ 2 = 10 * 0.216 * 0.16 = 0.3456.

Four Hit Probability:
C (4; 5) = 5! / ((5 – 4)! * 4!) = 5.
P (4; 5) = 5 * 0.6 ^ 4 * 0.4 = 5 * 0.216 * 0.16 = 0.2592.

Five Hit Probability:
P (5; 5) = 0.6 ^ 5 = 0.07772.

Let’s find the sum of the probabilities:
P (A) = 0.3456 + 0.2592 + 0.07772 = 0.68252.

Answer: The probability of getting a credit is 0.68252.