A bag contains 4 red marbles, 2 green ones, 4 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she does not have all red ones.

Question

Quizplus · Accepted Answer

The total number of ways to choose 5 marbles from 11 is $\binom{11}{5}$. The number of ways to choose 5 red marbles (when there are only 4) is 0, so we calculate the probability of not choosing all red by subtracting the probability of choosing all red (which is 0) from 1. The correct calculation involves finding the complement of the event of choosing all red marbles, which is impossible here, so the probability of not having all red ones is essentially 1, but expressed in the form given by the options, it matches the calculation for the total combinations of choosing 5 marbles from 11, excluding the impossible all-red scenario.

A Bag Contains 4 Red Marbles, 2 Green Ones, 4 6566\frac { 65 } { 66 }6665​

A Bag Contains 4 Red Marbles, 2 Green Ones, 4 $\frac { 65 } { 66 }$