Question 1138104: Suppose that you spin the double wheel pictured to the right. Assuming that the wheels are independent and each outcome is equally likely, determine the probability that you get red on both wheels.
A spinner consists of two concentric unequal circular wheels with the smaller one placed on the larger. The smaller wheel is divided into 8 equal sectors. The number of sectors for each color is as follows, where the label is listed first and the number of sectors is listed second: red, 3; blue, 2; yellow, 1; grey, 2. The larger wheel is divided into 12 equal sectors. The number of sectors for each color is as follows, where the label is listed first and the number of sectors is listed second: red, 4; blue, 2; yellow, 2; grey, 2; green, 2.
B=blue
G=green
Y=yellow
R=red
g=grey
The probability is
. (Type an integer or a simplified fraction.)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
There are 3 red out of 8 total in the smaller wheel.
The probability of spinning on red for this wheel is 3/8
There are 4 red out of 12 total in the larger wheel.
The probability of spinning on red for this wheel is 4/12 = 1/3
Your book states "Assuming that the wheels are independent" meaning that one wheel does not affect the other. The two events being independent allows us to multiply the probabilities found earlier.
M = event of spinning red on the smaller wheel
N = event of spinning red on the larger wheel
P(M) = 3/8
P(N) = 1/3
P(M and N) = probability of getting red on both wheels
P(M and N) = P(M)*P(N)
P(M and N) = (3/8)*(1/3)
P(M and N) = (3*1)/(8*3)
P(M and N) = 3/24
P(M and N) = 1/8
Answer as a fraction: 1/8
Extra info: This is equivalent to the decimal form 0.125 which converts to 12.5%
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