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 the box, what is the probability that the marble selected will be purple?  Select the correct option:  A) 3/20  B) 3/10  C) 9/20  D) 3/5  E) 9/10
The question asks us to select a purple marble from either of the boxes. Here we need to select a box first(either A or B) and then select the marble from the box. So these events are AND events i.e. both need to be done to select a purple marble from the box. For an AND event we multiply the probability of the events. Hence the probability equation can be written as:   P(Selecting a purple marble) = P(selecting a box) * P(selecting purple marble from the selected box)   The probability of selecting either of the box is the same = 1/2   =1/2∗30/50+1/2∗15/50=9/20.   Answer:9/20
<result>C</result>
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 the box, what is the probability that the marble selected will be purple?