Question

Celine is playing a game at the school carnival. There is a box of marbles, and each box has a white, a green, a blue, and an orange marble. There is also a fair 12-sided die labeled with the numbers 1 through 12. How many outcomes are in the sample space for pulling a marble out of the box and rolling the die?
48

32

16

8

Answer 1

There are four colors of marbles. There are 12 numbers on the dice. There is a 1/4 chance of pulling a specific color marble and a 1/12 chance of rolling a specific color. 1/4 times 1/12 is 1/48. There can be 48 outcomes.

Answer 2

There are 48 possible outcomes.

The first way to figure this problem out is to make a list for all the possible combinations.

(w = white, g = green, b = blue, and o = orange)

1, w; 2, w; 3, w; 4, w; 5, w; 6, w; 7, w; 8, w; 9, w; 10, w; 11, w; 12, w

1, g; 2, ; 3, g; 4, g; 5, g; 6, g; 7, g; 8, g; 9, g; 10, g; 11, g; 12, g

1, b; 2,b; 3, b; 4, b; 5, b; 6, b; 7, b; 8, b; 9, b; 10, b ; 11, b; 12, b

1, o; 2,o; 3,o; 4,o; 5,o; 6, o; 7, o; 8, o; 9,o ;10, o ;11, o 12, o

If you count all of these possibilities, you would come up with 48. Of course, this way takes a very long time, and there is an easier way.

Simply multiply 12 (The number of possibilities on the die) by 4 (The number of possible colors) to get 48.

Therefore, there are 48 possible outcomes in this situation.