Question

A bag contains 5 white and 3 black balls, another bag contains 4 white and 5 black balls. From any one of these bags a single draw of two balls is made. Find
the probability that one of them would be white and other black ball
Select one
O a 251/65
O b. Algebrical Ability
c. 268/503
O d. 275/504

Answer 1

bag1

no.of white balls=5

no.of black balls=3

p(white )=5÷8

p(black)=3÷8

bag 2

no.of white balls=4

no.of black balls=5

p(white balls)=4÷9

p(black )=5÷9

Answer 2

The correct option is D) $\frac{275}{504}$.

Step-by-step explanation:

Consider the provided information.

We have 2 bags which are equally likely to be selected.

Let P (A₁) and P (A₂) is the probability of the events drawing ball form bag 1 and bag 2 respectively.

Therefore, P (A₁) = P (A₂) = $\frac{1}{2}$

bag 1 contains 5 white and 3 black balls, and bag 2 contains 4 white and 5 black balls.

Thus, the required probability is:

$=\frac{1}{2}[\frac{^5C_1\times ^3C_1}{^8C_2}+\frac{^4C_1\times ^5C_1}{^9C_2}]$

$=\frac{1}{2}[\frac{15}{28}+\frac{20}{36}]$

$=\frac{1}{2}[\frac{135+140}{252}]$

$=\frac{275}{504}$

Hence, the correct option is D) $\frac{275}{504}$.

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