A bag contains 4 red marbles, 3 green ones, 3 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she has 2 green ones and 1 of each of the other colors.

Question

Quizplus · Accepted Answer

The probability is calculated by dividing the number of ways to achieve the desired outcome by the total number of possible outcomes. The desired outcome is selecting 2 green marbles, 1 red, 1 white, and 1 purple. The number of ways to choose these is $ \binom{3}{2} \times \binom{4}{1} \times \binom{3}{1} \times \binom{1}{1} = 3 \times 4 \times 3 \times 1 = 36 $. The total number of ways to choose any 5 marbles from 11 is $ \binom{11}{5} = 462 $. Thus, the probability is $ \frac{36}{462} = \frac{6}{77} $.

A Bag Contains 4 Red Marbles, 3 Green Ones, 3 677\frac { 6 } { 77 }776​

A Bag Contains 4 Red Marbles, 3 Green Ones, 3 $\frac { 6 } { 77 }$