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

Answer:

$P(X=3)$

And replacing we got:

$P(X=3)=(4C3)(0.3)^3 (1-0.3)^{4-3}=0.0756$

Step-by-step 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:

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

And we want to find this probability:

$P(X=3)$

And replacing we got:

$P(X=3)=(4C3)(0.3)^3 (1-0.3)^{4-3}=0.0756$