Question

По мішені стріляють 8 разів.Ймовірність влучення в мішень під час кожного пострілу дорівює 3/5.Яка ймовірність того,що з 8-ми пострілів у мішень влучать 5 разів?

Answer 1

Эта вероятность P=8!/(5!*3!)*(3/5)^5*(1-3/5)^5=7*8*243*32/(5^10)=0,04

Answer 2

Calculation of the Probability

To calculate the probability of hitting the target 5 times out of 8 shots, we can use the binomial probability formula. The formula is as follows:

P(x) = C(n, x) * p^x * (1-p)^(n-x)

Where: - P(x) is the probability of getting exactly x successes - n is the total number of trials (in this case, 8 shots) - x is the number of successes (in this case, 5 hits) - p is the probability of success in a single trial (in this case, 3/5)

Let's calculate the probability using this formula.

Calculation

Using the binomial probability formula, we can calculate the probability of hitting the target 5 times out of 8 shots.

P(5) = C(8, 5) * (3/5)^5 * (2/5)^3

Let's calculate this value.

Solution

Using the formula, we can calculate the probability as follows:

P(5) = C(8, 5) * (3/5)^5 * (2/5)^3

Calculating the combination:

C(8, 5) = 8! / (5! * (8-5)!) = 56

Substituting the values into the formula:

P(5) = 56 * (3/5)^5 * (2/5)^3

Calculating the values:

P(5) ≈ 0.164

Therefore, the probability of hitting the target 5 times out of 8 shots is approximately 0.164.

Please note that the calculation assumes each shot is independent and the probability of hitting the target remains constant for each shot.

Let me know if there's anything else I can help you with!