Question

Audiooplying Theoretical ...ColorFull ScreenHighlightsSpeakXA bag of marbles contains 2 white, 3 black, 1 red, and 4 blue marbles. Cade sélects two marbles from the bag at random andthen replaces both marbles. He does this a total of 30 times. What is a reasonable prediction for the number of times he willselect a blue marble followed by a black marble?

Answer 1

We are given the following information.

White marbles = 2

Black marbles = 3

Red marbles = 1

Blue marbles = 4

The total number of marbles are

Total marbles = 2+3+1+4 = 10

Cade selects two marbles from the bag at random with replacement.

The probability of selecting a blue marble is given by

`P(blue)=(blue\;marbles)/(total\;marbles)=(4)/(10)=(2)/(5)`

The probability of selecting a black marble is given by

`P(black)=(black\;marbles)/(total\;marbles)=(3)/(10)`

The probability of selecting a blue marble followed by a black marble is given by

`\begin{gathered} P(blue\;and\;black)=P(blue)* P(black \\ P(blue\;and\;black)=(2)/(5)*(3)/(10)=(6)/(50)=(3)/(25) \end{gathered}`

So, the probability of selecting a blue marble followed by a black marble is 3/25

He does this a total of 30 times.

`(3)/(25)*30=3.6`

Therefore, the reasonable prediction for the number of times he will select a blue marble followed by a black marble is 3.6 times.