Question

1. There are 5 gray, 4 red, 5 white, 2 green, and 2 navy marbles in a hat. You are going to
draw one marble and replace it and draw again. Find the probability for the following
events.
a) Draw red and green marbles.
b) Draw navy and white marbles.
c) Draw gray and gray marbles.

Answer 1

Answer:

(a). $\frac{2}{81}$ ; (b). $\frac{5}{162}$ ; (c). $\frac{25}{324}$

Step-by-step explanation:

To find the probability of two independent events we have to find the product of each event occurred.

Total outcome: 5 gray + 4 red + 5 white + 2 green + 2 navy = 18

a). Probability to draw the red marble is $\frac{4}{18}$ = $\frac{2}{9}$

    Probability to draw the green marble is $\frac{2}{18}$ = $\frac{1}{9}$

Probability to draw red and green marbles is $\frac{2}{9}$ × $\frac{1}{9}$ = $\frac{2}{81}$ ;

b). Probability to draw the navy marble is $\frac{2}{18}$ = $\frac{1}{9}$

    Probability to draw the white marble is $\frac{5}{18}$

Probability to draw navy and white marbles is $\frac{5}{18}$ × $\frac{1}{9}$ = $\frac{5}{162}$ ;

c). Probability to draw the gray marble is $\frac{5}{18}$

Probability to draw gray and gray marbles is $\frac{5}{18}$ × $\frac{5}{18}$ = $\frac{25}{324}$ ;