Probability Review

Question

Consider a bag of 7 blocks. Each block has a different color. The colors are Red, Orange, Yellow, Green, Blue, Indigo, and Violet. You reach into the bag of 7 blocks and pull out 2 blocks. What is the probability that at least one of the blocks you pulled out is Red, Orange, or Yellow?

Answer 1

To do this problem, we assume the opposite: that none of the blocks are red, orange or yellow. There is a 4 out of 7 chance that the first block you pull out is not red, orange, or yellow, because 4 out of 7 aren't these colors. Then you pull out a second block. There is now a 3 out of 6 chance the second block is not red, orange, or yellow. Multiply 4 out of 7 with 3 out of 6 to get the probability that none of the blocks are red, orange, or yellow.

Lastly, notice that P(none are red, orange, or yellow) + P(at least one are red, orange, or yellow) = 1

So, to find the probability that at least on is red, orange, or yellow, subtract the probability that none are red, orange, or yellow from 1.