Question

A random variable X counts the number of successes in 20 independent trials. The probability that any one trial is unsuccessful is 0.42. What is the probability of exactly eight successful trials

Answer 1

Answer:

$P(X=8)$

And using the probability mass function we got:

$P(X=8)=(20C8)(0.58)^8 (1-0.58)^{20-8}=0.0486$

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=20, p=1-0.42=0.58)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

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

And we want to find this probability:

$P(X=8)$

And using the probability mass function we got:

$P(X=8)=(20C8)(0.58)^8 (1-0.58)^{20-8}=0.0486$