Question

On a store counter are exactly two boxes containing only purple marbles and yellow marbles. Box A has 30 purple marbles and 20 yellow marbles; box B has 15 purple marbles and 35 yellow marbles. If Melanie randomly selects one of the boxes and then randomly selects one marble from that box, what is the probability that the marble selected will be purple?

Answer 1

Answer: Our required probability would be 0.35.

Step-by-step explanation:

Since we have given that

Number of boxes = 2

Number of purple marbles in Box A = 30

Number of yellow marbles in Box A = 20

Number of purple marbles in Box B = 15

Number of yellow marbles in Box B = 35

So,  If Melanie randomly selects one of the boxes and then randomly selects one marble from that box.

Probability that the marble selected will be purple is given by

$\dfrac{1}{2}\times \dfrac{20}{50}+\dfrac{1}{2}\times \dfrac{15}{50}\\\\=\dfrac{1}{2}(\dfrac{20+15}{50})\\\\=\dfrac{1}{2}\times \dfrac{35}{50}\\\\=\dfrac{35}{100}\\\\=0.35$

Hence, our required probability would be 0.35.