Question

Монету подбрасывают 11 раз. найти вер-ть того, что герб выпадет 5 раз.

Answer 1

Чисто рандом и ничего больше :D

Answer 2

To calculate the probability of getting exactly 5 heads (gerb) when flipping a coin 11 times, we can use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Where: P(X = k) is the probability of getting exactly k successes (5 heads in this case), n is the number of trials (11 coin flips), k is the number of successes we want (5 heads), p is the probability of success on a single trial (probability of getting a head, assuming a fair coin, p = 0.5), and ( n choose k ) = n! / (k! * (n - k)!) is the binomial coefficient.

Let's calculate it:

P(X = 5) = (11 choose 5) * (0.5)^5 * (1 - 0.5)^(11 - 5)

To calculate (11 choose 5), we use the formula: (11 choose 5) = 11! / (5! * (11 - 5)!)

(11 choose 5) = 11! / (5! * 6!) (11 choose 5) = (11 * 10 * 9 * 8 * 7) / (5 * 4 * 3 * 2 * 1) (11 choose 5) = 462

Now, plug in the values:

P(X = 5) = 462 * (0.5)^5 * (0.5)^6 P(X = 5) = 462 * 0.03125 * 0.015625 P(X = 5) = 0.024262...

So, the probability of getting exactly 5 heads (gerb) when flipping the coin 11 times is approximately 0.02426 or 2.426%.