Question

A bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 blackboll One ball is drawn from each bag, find the probability that i) both are whiteii)both are black iii) one is white and another is black

Answer 1

Let white balls be w, and black balls be b;

In the first bag;

`n(w)=5,n(b)=3,n(T)=8`

But, in the second bag;

`n(w)=4,n(b)=6,n(T)=10`

(i) The probability that both balls drawn from each bag are white is;

`\begin{gathered} P(w\text{ and }w)=(5)/(8)*(4)/(10) \\ P(w\text{ and }w)=(20)/(80) \\ P(w\text{ and }w)=(1)/(4) \end{gathered}`

(ii) The probability that both balls drawn from each bag are black is;

`\begin{gathered} P(b\text{ and }b)=(3)/(8)*(6)/(10) \\ P(b\text{ and }b)=(18)/(80) \\ P(b\text{ and }b)=(9)/(40) \end{gathered}`

(iii) The probability that one is white and another is black is;

`\begin{gathered} P(w\text{ and }b)=((5)/(8)*(6)/(10))+((3)/(8)*(4)/(10)) \\ P(w\text{ and }b)=(30)/(80)+(12)/(80) \\ P(w\text{ and }b)=(42)/(80) \\ P(w\text{ and }b)=(21)/(40) \end{gathered}`