Question

At a game booth, a student gets a box of candy as the 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? (1 point)

Select one:
a. (10/40) * (9/39)
b. (10/40) * (10/39)
c. (10/40) + (9/39)
d. (10/40) + (10/39)

Answer 1

a. (10/40) * (9/39)

Explanation:

Since, the total number of white box = 10,

Red box = 10,

Green box = 10,

And, Blue box = 10,

Thus, the total number of boxes = 10 + 10 + 10 + 10 = 40

The probability of receiving white box by first winner = White box / Total box = 10/40

Since, the replacing is not allowed ( Because, here boxes are allotted )

Thus, the remaining white box = 10 - 1 = 9,

And, the remaining total boxes = 40 - 1 = 39,

Thus, the probability of receiving white box by second winner = Remaining white box / Remaining total box = 9/39

Hence, the probability of the first winner receiving a white box and the second winner also receiving a box of the same color = 10/40 * 9/39

Which is required expression.