Question

lysha is at a local library with her best friend. they've noticed a lot of cute boys in the library, and alysha bets that of the next twenty people to enter the library, exactly 12 will be cute boys. assuming there is a 50% chance that the next person to walk into the library is a cute boy, what is the probability that alysha will win the bet?

Answer 1

Using the binomial distribution, there is a 0.1201 = 12.01% probability that Alysha will win the bet.

What is the binomial distribution formula?

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

• x is the number of successes.

• n is the number of trials.

• p is the probability of a success on a single trial.

For this problem, the parameters are given as follows:

n = 20, p = 0.5.

She wins the bet if there are 12 boys, hence the probability is P(X = 12), found as follows:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 12) = C_{20,12}.(0.5)^{12}.(0.5)^{8} = 0.1201$

0.1201 = 12.01% probability that Alysha will win the bet.

More can be learned about the binomial distribution at brainly.com/question/24863377

#SPJ1