SOLUTION: In a Christmas display, the probability that all the lights are the same colour is 0.50, that two colours are used is 0.40 and that three or more colours are used is 0.10. If a sa

Algebra ->  Probability-and-statistics -> SOLUTION: In a Christmas display, the probability that all the lights are the same colour is 0.50, that two colours are used is 0.40 and that three or more colours are used is 0.10. If a sa      Log On


   

Question 1142247: In a Christmas display, the probability that all the lights are the same colour is 0.50, that two colours are used is 0.40 and that three or more colours are used is 0.10. If a sample of 10 displays is selected, find the probability that 5 have only 1 colour of light, 3 have two colours and 2 have 3 or more colours.
Answer by greenestamps(13195) About Me  (Show Source):
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Let x be the condition that one color is used, y the condition that 2 colors are used, and z the condition that 3 or more colors are used. Then the probability we want is the coefficient of the

%28x%5E5%29%28y%5E3%29%28z%5E2%29

term in the expansion of

%28.5x%2B.4y%2B.1z%29%5E10

The multinomial theorem says that number is



You can do the calculations on your calculator.