Question

There is a bag containing 4 red marbles, 3 green marbles, 2 white marbles, and 1 purple marble. If you grab 5 marbles at a time, find the probabilities of the following.

b) Two red marbles and one of each color.
a) All green marbles.
c) At most one green marble.

Answer 1

To find the probability of grabbing two red marbles and one of each color, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.

Step-by-step explanation:

To find the probability of grabbing two red marbles and one of each color, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes. The number of favorable outcomes is the number of ways to choose 2 red marbles out of 4 and 1 green, 1 white, and 1 purple marble out of the remaining 9. This can be calculated using combinations. The total number of possible outcomes is the number of ways to choose 5 marbles out of 10, which can also be calculated using combinations. So, the probability is:

P(Two red marbles and one of each color) = (Number of favorable outcomes) / (Total number of possible outcomes)