Suppose I pick a jelly bean at random from a box containing two red and ten blue ones. I record the color and put the jelly bean back in the box. What is the probability of getting a red jelly bean both times if I do this twice? (Round your answer to three decimal places.)

Answer:The probability of getting a red jelly bean both of the times is 0.028.Step-by-step explanation:First we have that in the box are 12 jelly beans having 2 red and 10 blue. The probability of getting one of the red jelly beans are the sum of the probability of the 2 red jelly beans, that is:[tex]ProbabilityRed=\frac{1}{12} +\frac{1}{12}=\frac{2}{12}[/tex]Now we can calculate the probability of getting the red jelly bean twice, this will be the product of the probability of getting each one, is the same probability for the second chance because we are getting the jelly bean back in the box, this is:[tex]ProbabilityBothRed=\frac{2}{12} *\frac{2}{12}=\frac{4}{144}  =\frac{1}{36} =0.028[/tex]Now we have that the probability of getting a red jelly bean both of the times is 0.028.