Question

There are 4 yellow marbles, 3 red marbles, and 1 blue marble in a bag. If I were to draw a marble out of the bag 32 times, how many times would I get red?

Answer 1

The expected number of times a red marble will be selected is 12.

Explanation:

The number of marbles in a bag are:

Yellow = 4

Red = 3

Blue = 1

Total = 8

Le the random variable X be defined as the number of red marble selected.

The probability of selecting a red marble is:

`P(red)=(3)/(8)`

A marble is selected from the bag n = 32 times.

The color of the marble selected at the nth draw is independent of the previous draw.

The success is defined as selecting a red marble.

The random variable X thus follows a Binomial distribution with parameters n = 32 and p =
`(3)/(8)`.

The expected value of a Binomial random variable is:

`E(X)=np`

Compute the expected number of times a red marble will be selected in 32 draws as follows:

`E(X)=np`

`=32*(3)/(8)\\=12`

Thus, the expected number of times a red marble will be selected is 12.