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 $\frac{1}{15}$

Step-by-step 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  

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

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

Step 2: the probability of drawing red ball will be

                $P_{2}(r e d)=\frac{2}{9}$

Now the probability that both the drawn balls are red is

               $P(r e d)=P_{1} \times P_{2}=\frac{3}{10} \times \frac{2}{9}=\frac{1}{15}$

Hence, the probability of getting 2 red marbles is $\frac{1}{15}$