Question

At a game booth, a student gets a box of candy as a prize for winning a game. The boxes come in four colors: white, red, green, and blue. There are 10 boxes of each color All the boxes are equally likely to be given away as prizes. Which expression shows the probability of the first winner receiving a white box and the second winner also receiving a box of the same color?
A - (8/42) x (8/31)
B - (8/32) + (8/31)
C - (8/32) + (7/31)
D- (8/32) x (7/31)

Answer 1

None of the answers seem correct, but judging by the options, it looks like there are 8 boxes of each color. Let's stick with 10 and make this clear:

For each extraction, you have to compute the number of "good" outcomes and the number of all possible outcomes. The probability of a particular event is the ratio between the two.

So, for the first student, we have 10 white boxes available over 40 possible boxes (10 white, 10 red, 10 green and 10 blue). So, the first student receives a white box with probability 10/40. Note that, if there were 8 boxes for each color, you would have 8 white boxes over 32 total boxes, and so the ratio would be 8/32.

The second student is left with the following boxes: 9 white (the first student received one of the white, 10 red, 10 green and 10 blue. So, 39 boxes in total. The probability of receiving a white one is thus 9/39. Note that, if there were 8 boxes for each color, you would have 7 white boxes over 31 total boxes, and so the ratio would be 7/31.

Now, if you want two events to happen one after the other, you have to multiply their probability. So, the answer is 10/40 * 9/39. Note that, if there were 8 boxes for each color, you would have 8/32 * 7/31.

So, the answer would be D, if the "ten boxes for each color" is a typo, and you actually meant "eight boxes for each color". Otherwise, none of the options is correct.