Question

you have a jar of marbles in front of you two are cordovan 9 are yellow 3 are white and seven all red what is the probability as a fraction of selecting a marble that is white or yellow followed by a marble that is cordovan?

Answer 1

The probability can be written as;

`\begin{gathered} Pr(\text{White or yellow followed by cordovan)= Pr(White or yellow) x Pr(Cordovan)} \\ =\lbrack(Pr(white)+Pr(yellow))\rbrack* Pr(Cordovan) \end{gathered}`

Now, we know that;

`\begin{gathered} Pr(\text{White)}=(3)/(21)=(1)/(7) \\ Pr(\text{Yellow)}=(9)/(21)=(3)/(7) \\ (Pr(white)+Pr(yellow))=(1)/(7)+(3)/(7)=(4)/(7) \\ Pr(\textCordovan (2)/(20) \end{gathered}`

Therefore, the probability as a fraction of selecting a marble that is white or yellow followed by a marble that is cordovan is (assuming without replacement)

`\begin{gathered} (4)/(7)*(2)/(20)=(8)/(140) \\ \\ =(2)/(35) \end{gathered}`

Thus the probability is 2/35