Question

A box contains 4 orange pencils, 5 yellow pencils, and 3 green pencils. Two pencils are selected, one at a time, with replacement. Find the probability that the first pencil is green and the second pencil is yellow. Express your answer as a decimal, rounded to the nearest hundredth.

Answer 1

For finding 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 we pick a pencil, we have to find the probability that it is a green pencil.

Probability = favorable outcomes / total possible outcomes = 3 green / (5 yellow + 3 green +4 orange)

= 3 green pencils / 12 total pencils

Thus, the probability of the first event is 3/12 that is 1/4

According to the question, we want to pick a yellow pencil 2nd time, but we also replace it that is after first event selected pencil is returned to the place from where it was selected . So total pencils is 12 now (no change)

Thus, probability of the second event = probable outcomes/ total outcomes =

5 yellow pencils/(5 yellow +3 green+4 orange pencils)

= 5 / 12

Therefore, the second event's probability is 5/12

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

(1/4) * (5/12) = 5/48

Or we can write 5/48 as 0.104 (rounded)

So required probability of first green then yellow is 5/48