# 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.