Question

A bag contains 3 red, 4 yellow, and 5 blue marbles. Two marbles are randomly selected from the bag with replacement .1) Find the probability that:They are the same color 2) at least one is red

Answer 1

Answer:

The probability that they are of the same colour is 19/66

The probability that at least one is red is 5/11

Step-by-step explanation:

Given that there are:

3 red, 4 yellow, and 5 blue marbles

Total number of marbles = 12

Two marbles are randomly selected,

1.

The probability that they are of the same colour is:

(Probability that both are red) plus (the probability that both are yellow) plus (the probability that both are blue)

`\begin{gathered} =((3)/(12)*(2)/(11))+((4)/(12)*(3)/(11))+((5)/(12)*(4)/(11)) \\ \\ =(1)/(22)+(1)/(11)+(5)/(33) \\ \\ =(19)/(66) \end{gathered}`2.

The probability that at least one is red is:

1 - probability that non is red.

`\begin{gathered} =1-((9)/(12)*(8)/(11)) \\ \\ =1-(6)/(11) \\ \\ =(5)/(11) \end{gathered}`