A game consits of spinning a spinner and then rolling a numb

A game consits of spinning a spinner and then rolling a number cube. The spinner is equally likely to land on a ny 1 of of the 4 colors red, yellow, green, or blue. The number cube is equally likely to land with any 6 sides labeled 1 through 6 up. To win the game, a contestan must either spin a red or a yellow and roll a 1 or a 2 or spin a green or blue and roll a 5 or a 6. What is the probability of winning this game? Explain why you can use fraction arithmetic to solve this problem.

Solution

What is the probability of winning this game?

for each colo is 1/4

and for each land is 1/6

sp for win

a contestan must either spin a red or a yellow and roll a 1 or a 2 or spin a green or blue and roll a 5 or a 6

2/4 * 2/6 + 2/4 * 2/6

1/6 + 1/6

1/3