Three urns contain 6 red, 4 black; 4 red, 6 black and 5 red, 5 black marbles respectively. One of the urns is selected at random and a marble is drawn from it. If the marble drawn is red, then the probability that it is drawn from the first urn is
Answer & explanation
Correct answer: option 4
| Urn 1 | Urn 2 | Urn 3 |
|
6 : Red |
4 : Red |
5 : Red |
|
$P(\frac{R}{U_1})$ $= \frac{6}{10}$ |
$P(\frac{R}{U_2})$ $= \frac{4}{10}$ |
$P(\frac{R}{U_3})$ $= \frac{5}{10}$ |
no. of urns = 3
$P(U_1) = \frac{1}{3} = P(U_2) = P(U_3)$
Ui → selecting ith urn
$P(\frac{U_1}{R}) = \frac{P(U_1) P(\frac{R}{U_1})}{\sum\limits_{i=1}^{3} P(U_i) P(\frac{R}{U_i})} = \frac{\frac{1}{3} \times \frac{6}{10}}{\frac{1}{3} \times \frac{6}{10}+\frac{1}{3} \times \frac{4}{10}+1 \times \frac{5}{10}}$
$= \frac{6}{15} = \frac{2}{5}$
Option: 4