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 8 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?

8/32 * 8/31
8/32 * 7/31
8/32 + 7/31
8/32 + 8/31

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 8 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?

8/32 * 8/31
8/32 * 7/31
8/32 + 7/31
8/32 + 8/31

victoriasushchik · Answer

There are 4 colors and 8 boxes of each color. That means there are 32 boxes altogether.
The winner is the first to get a box.
When he gets a box, his box is picked out of the 32. Since there are 8 white boxes, the probability of picking a white box for the winner is 
P(white for winner) = 8/32

Once the winner got a white box, now there are 31 boxes left and of which 7 are white.
Now you take a box for the second place.
P(white for second place) = 7/31

To find the final answer, MULTIPLY the two individual probabilities.

victoriasushchik · Answer

56/124  you multiply the probabilities, not add them.