Question

A bag contains 5 balls: 3 blue, 1 red, and 1 yellow. You select a ball at random 4 times, replacing the ball after each selection. Calculate the theoretical probability of getting a blue ball exactly 3 times

Answer 1

`P(X=3)`

And replacing we got:

`P(X=3)=(4C3)(0.3)^3 (1-0.3)^(4-3)=0.0756`

Explanation:

Let X the random variable of interest "number of times that we select a blue ball", on this case we now that:

`X \sim Binom(n=4, p=3/10)`

The probability is always the same since we replace the ball selected in each trial.

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=(n!)/((n-x)! x!)`

And we want to find this probability:

`P(X=3)`

And replacing we got:

`P(X=3)=(4C3)(0.3)^3 (1-0.3)^(4-3)=0.0756`