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

Question

Quizplus · Accepted Answer

The probability of grabbing at least 1 green marble is easier to calculate by finding the complement, which is the probability of not grabbing any green marbles, and subtracting it from 1. There are 9 marbles that are not green out of a total of 9 marbles, so the probability of not picking a green marble in 5 tries is $\frac{7}{9} \times \frac{6}{8} \times \frac{5}{7} \times \frac{4}{6} \times \frac{3}{5} = \frac{1}{6}$. Therefore, the probability of picking at least one green marble is $1 - \frac{1}{6} = \frac{5}{6}$.

A Bag Contains 4 Red Marbles, 2 Green Ones, 2 29\frac { 2 } { 9 }92​

A Bag Contains 4 Red Marbles, 2 Green Ones, 2 $\frac { 2 } { 9 }$