Question

Suppose that a box contains 5 red blocks, 4 blue blocks, and 3 green blocks. Suppose that 6 are drawn one after another without replacement. What is the probability that exactly 3 are blue?

Answer 1

To find the probability of drawing exactly 3 blue blocks from a total of 6 without replacement, we use combinations to determine the different ways to choose 3 blue blocks from 4 and 3 non-blue blocks from 8, then divide by the total number of ways to choose 6 blocks from 12.

Step-by-step explanation:

The question asks us to calculate the probability of drawing exactly 3 blue blocks from a box that contains 5 red blocks, 4 blue blocks, and 3 green blocks, without replacement, among 6 total draws.

To solve this, we need to use combinations to determine the number of ways 3 blue blocks can be chosen from 4, and the remaining 3 blocks can be chosen from the 8 non-blue blocks. The probability would then be calculated as the combination of successful outcomes over the combination of all possible outcomes of drawing 6 blocks from 12.

The calculation would look something like this:

P(exactly 3 blue) = (Combination of choosing 3 blue blocks) * (Combination of choosing 3 non-blue blocks) / (Combination of choosing 6 blocks from all 12).