Question

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Suppose there are 15 candles. 5 are red and 10 are green. 4 are selected to be put on display on a shelf.
a. What is the probability that if 4 candles are selected at random that they will alternate colours?
b. What is the probability that if the 4 candles are selected at random that they will be all red or all green?

Answer 1

a)

probability that if 4 candles are selected at random that they will alternate colors

=P(select 2 red and 2 green and arrange them in alternate order)

=((₅C₂)*(₁₀C₂)/(₁₅C₄))*(2/6) =(10*45/1365)*(1/3)=0.1099

(other way to solve: P(alternate )=P(RGRG)+P(GRGR)

=(5*10*4*9)/(15*14*13*12)+(10*5*9*4)/(15*14*13*12) =0.1099

b)

probability that if the 4 candles are selected at random that they will be all red or all green

=P(all 4 red)+P(all 4 green) =(₅C₄)/(₁₅C₄)+(₁₀C₄)/(₁₅C₄)=(1/1365)+(210/1365)=211/1365=0.1546