You are spinning a spinner that can land on three colors re

You are spinning a spinner that can land on three colors - red, blue and yellow. For this spinner P(red) = 2/6 = 1/3, P(blue) = 1/6, and P(yellow) = 3/6 = 1/2, you spin the spinner 10 times. What is the probability that you spin red five times, blue three times and yellow two times?

Solution

this is easy

if you spin the spinner 10 times and you have the probabilities for each color you just need to see how many times have the color that you need or you wish to know

for this is

P red = 1/3 and you need 5 times

P blue = 1/6 and you need 3 times

P yellow = 1/2 and you need 2 times

so the probability for 5 red , 3 blue and 2 yellow is

(1/3)^5 * (1/6) ^3 * (1/2)^2

0.004115 * 0.0046296 * 0.25

4.76299 x 10 ^-6

Probabilitie is 4.76299 x 10 ^-6