Abox contains 5 green pencils and 7 yellow pencils. two pencils are chosen at random from the box without replacement. what is the probability they are both yellow?

To find the probability of two events happening, we must multiply the probability of each separate event happening by the other.

So, for the first time that you pick a pencil, we have to find the probability that it is a yellow pencil. 

Probability = favorable outcomes / total possible outcomes = 7 yellow / 7 yellow + 5 green = 7 yellow pencils / 12 total pencils

Thus, the probability of the first event is 7/12.

According to the question, we want to pick a yellow pencil both times, but we don't replace it.  So, assuming we pick a yellow pencil, we have to subtract that from the next calculation.

Thus, probability of the second event = probable outcomes/ total outcomes = 6 yellow pencils / 6 yellow + 5 green pencils = 6 / 11

Therefore, the second event's probability is 6/11.

To find the total probability, we must multiply the two fractions together.

7 / 12 * 6 / 11 = 42 / 132

But, we want to simplify this fraction, so:

42 / 132 = 42 ÷ 6 / 132 ÷ 6 = 7/22

Thus, the probability is 7/22, or approximately 32%.

Hope this helps! :)