Question

A bag contains 9 yellow marbles, 4 blue marbles, 3 green marbles, 5 red marbles, and 7 purple marbles. A marble is chosen at random, not replaced, then another marble is chosen. Find the P(red, then yellow)

Answer 1

Given:

• Number of yellow marbles = 9

,

• Number of blue marbles = 4

,

• Number of green marbles = 3

,

• Number of red marbles = 5

,

• Number of purple marbles = 7

A marble is chosen at random, not replaced, then another marble is chosen. Find the P(red, then yellow).

Probability that the first marble picked is red:

$P(red)=\frac{\text{ number of red marbles}}{total\text{ number of marbles}}$

Where:

total number of marbles = 9 + 4 + 3 + 5 + 7 = 28

Number of red = 5

Hence, we have:

$P(red\text{ first})=\frac{5}{28}$

Now, for the next marble to be a yellow marble given that the red marble was not replaced, we have:

$P(yellow\text{ next\rparen=}\frac{number\text{ of yellow marbles}}{total\text{ marbles - 1}}=\frac{9}{28-1}=\frac{9}{27}=\frac{1}{3}$

Hence, for P(red, then yellow), the probability will be:

$P(red,then\text{ yellow\rparen= }\frac{5}{28}*\frac{1}{3}=\frac{5}{28*3}=\frac{5}{84}$

ANSWER:

$P(red,\text{ then yellow\rparen = }\frac{5}{84}$