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  • Bag I contains 3 black and 2 white balls, Bag II contains 2 black and 4 white balls. A bag and a ball are selected at random. Determine the probability of selecting a black ball.

Bag I contains 3 black and 2 white balls, Bag II contains 2 black and 4 white balls. A bag and a ball are selected at random. Determine the probability of selecting a black ball.

Answers (1)

Given-

Bag I= [3Black, 2White], Bag II= [2 black, 4 white]

Let E1 be the event that bag I is selected
E2 be the event that bag II is selected
E3 be the event that a black ball is selected

Therefore,

\\ \Rightarrow P(E 1)=P(E 2)=\frac{1}{2} \\ P\left(E \mid E_{2}\right)=\frac{3}{5} \\ P\left(E \mid E_{2}\right)=\frac{2}{6}=\frac{1}{3} \\ \therefore P(E)=P\left(E_{1}\right) \cdot P\left(E \mid E_{1}\right)+P\left(E_{2}\right) \cdot P\left(E \mid E_{2}\right) \\ =\frac{1}{2} \times \frac{3}{5}+\frac{1}{2} \times \frac{2}{6} \\ =\frac{3}{10}+\frac{2}{12} \\ =\frac{18+10}{60} \\ =\frac{28}{60} \\ =\frac{7}{15}

Posted by

infoexpert22

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