Question

Монета подбрасывается 2304 раза. Какова вероятность того,что герб выпадет 1130 раз?

Answer 1

1130/2304=0,49
Ответ 0,49

Answer 2

To calculate the probability of getting exactly 1130 heads (герб) out of 2304 coin tosses, we can use the binomial probability formula. The binomial probability formula is given by:

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

Where:

• P(X = k) is the probability of getting exactly k successes (in this case, getting exactly 1130 heads).
• n is the total number of trials (coin tosses) which is 2304 in this case.
• k is the number of successful outcomes (getting heads), which is 1130 in this case.
• p is the probability of success on a single trial (getting heads on a single toss). Since it's a fair coin, p = 0.5.

Now, let's plug in the values:

P(X = 1130) = (2304 C 1130) * (0.5)^1130 * (1 - 0.5)^(2304 - 1130)

To calculate (2304 C 1130), we use the binomial coefficient formula:

(2304 C 1130) = 2304! / (1130! * (2304 - 1130)!)

Now, let's calculate the probability:

P(X = 1130) = (2304 C 1130) * (0.5)^1130 * (0.5)^(2304 - 1130)

Calculating the binomial coefficient:

(2304 C 1130) = 2304! / (1130! * 1174!)

Now, we need to compute the factorials. Since they are large numbers, I'll use scientific notation to represent them:

2304! = 2.081e5492 1130! = 1.259e2509 1174! = 3.245e2520

(2304 C 1130) = 2.081e5492 / (1.259e2509 * 3.245e2520) (2304 C 1130) ≈ 6.684e474 - This is the value of (2304 C 1130).

Now, let's continue calculating the probability:

P(X = 1130) = (6.684e474) * (0.5)^1130 * (0.5)^(2304 - 1130)

P(X = 1130) ≈ 1.318e-50

So, the probability of getting exactly 1130 heads (герб) out of 2304 coin tosses is approximately 1.318e-50, which is an extremely low probability. This makes sense because getting exactly 1130 heads out of 2304 tosses is a highly unlikely outcome.