Question

If a fair coin is flipped 50 times, what is the probability of 25 heads?

Answer 1

Answer: Probability of getting 25 heads is 0.11 or 11%.

Step-by-step explanation:

Since we have given that

A fair coin is tossed 50 times.

So, here, N = 50

Probability of getting a head =
`(1)/(2)`

Probability of getting a tail =
`(1)/(2)`

So, we will apply "Binomial distribution":

Let X is the number of getting heads.

`P(X=25)=^(50)C_(25)p^(25)q^(25)`

Here,
`p=0.5,\ q=0.5`

So, it becomes,

`P(X=25)=^(50)C_(25)(0.5)^(25)* (0.5)^(25)\\\\P(X=25)=0.1122\\\\P(X=25)\approx 0.11`

Hence, Probability of getting 25 heads is 0.11 or 11%.

Answer 2

The correct answer is 0.11.

Step-by-step explanation:
This is binomial, as there are a fixed number of trials, the probability of each trial is independent, and there are only two outcomes. Since that is the case, we will calculate:

`_nC_r(p)^r(1-p)^(n-r)=_(50)C_(25)(0.5)^(25)(1-0.5)^(50-25) \\ \\=(50!)/(25!25!)(0.5^(25))(0.5^(25))=0.11`