Question

a bag contains 3 red marbles,3 green marbles, 3 yellow marbles and 1 white marble. You randomly draw a marble from the bag. Without replacing it, you draw a second marvel. What is the probability that you draw two red marbles?

Answer 1

The probability of getting 2 red marbles is
`(1)/(15)`

Explanation:

A bag contains 3 red marbles, 3 green marbles, 3 yellow marbles and 1 white marble. You randomly draw a marble from the bag. Without replacing it, you draw a second marvel.

Need to find out the probability that you draw two red marbles.

Total number of marbles = 3 R + 3 G + 3 Y + 1 W = 10

Step 1: Let one ball is drawn then the probability that the drawn ball is red is

`P_(1)(r e d)=\frac{\text { no. of red balls }}{\text { total no. of balls }}=(3)/(10)`

Now the second ball is drawn without replacing the first drawn ball

Step 2: the probability of drawing red ball will be

`P_(2)(r e d)=(2)/(9)`

Now the probability that both the drawn balls are red is

`P(r e d)=P_(1) * P_(2)=(3)/(10) * (2)/(9)=(1)/(15)`

Hence, the probability of getting 2 red marbles is
`(1)/(15)`