Chapter 12.5, Problem 1ACYP

To determine

To find: The probability of blue and green marbles.

Answer to Problem 1ACYP

The probability of blue and green marbles is $\frac{18}{441}$

Explanation of Solution

Given information:

A bag contains 6 black marbles, 9blue marbles, 4 yellow marbles, and two green marbles.

A marble is selected, replaced and a second marble is selected.

Formula used:

  $p\left(\text{A and B}\right)=p\left(\text{A}\right)\cdot p\left(\text{B}\right)$

Calculation:

First marble: $p\left(blue\right)=\frac{9}{21}\frac{\text{number of blue marbles}}{\text{total number of marbles}}$

Second marble: $p\left(green\right)=\frac{2}{21}\frac{\text{number of green marbles}}{\text{total number of marbles}}$

P(blue,green)= p(blue) $\cdot$ p(green)

P(blue, green) = $\frac{9}{21}\cdot \frac{2}{21}$

P(blue, green) = $\frac{18}{441}$

Therefore,

The probability of blue and green marbles is $\frac{18}{441}$ .