Question

An urn A contains 8 black and 5 white balls. A second urn B contains 6 black and 7 white balls. A blindfolded person is asked a ball selecting one of the urns, the probability that the ball drawn is black is:
A. $\dfrac{5}{{13}}$
B. $\dfrac{6}{{13}}$
C. $\dfrac{7}{{13}}$
D. $\dfrac{9}{{13}}$

Answer 1

Hint: The given question needs to be solved for the probability of the given situation in which different colored balls are there, and the probability of black ball drawn is asked. For this type of question we need to use probability formulae in which the ratio of probability is given by the favorable outcome to the total outcomes.

Complete step by step solution:
The given question says that there are two earn which contains 13 balls each, and in each earn there are black balls as well as white balls, here we have to find for the black ball probability when a blind fold person asked to select the balls,
Here first we have to write the statements, on plotting statement we get:
\[
   \Rightarrow Urn \, A :\,8B + 5W = 13balls \\
   \Rightarrow Urn \, B :6B + 7W = 13balls \\
   \Rightarrow \text{selection of an urn} = \dfrac{1}{2} \;
 \]
Now for getting the probability we have to solve for the probability of black ball in urn1 and urn2 which will be multiply by the probability of choosing the urn, on solving we get:
\[ \Rightarrow \text{Probability that the one drawn ball is black} = \dfrac{1}{2}\left[ {\dfrac{8}{{13}} + \dfrac{6}{{13}}} \right] = \dfrac{1}{2}\left[ {\dfrac{{14}}{{13}}} \right] = \dfrac{7}{{13}}\]
Hence this is our required probability.
So, the correct answer is “Option C”.

Note: The given question needs to be solved by these steps, only as probability needs to be solved by using the favorable outcome to the total outcome, and here there are two probability combined together, one is of getting the black ball and the other one is getting the urn.