Question

An urn contains $3$ red and $5$ blue balls. The probability that two balls are drawn in which 2nd ball drawn is blue without replacement is

• A. $\frac{5}{16}$
• B. $\frac{5}{56}$
• C. $\frac{5}{8}$
• D. $\frac{20}{56}$

Answer 1

The correct option is C

$\frac{5}{8}$

Explanation for the correct option:

Step: 1 Calculate the probability of first ball is red and second ball is blue.

There are $3$ red and $5$ blue balls in the urn.

Therefore, total balls in that urn is $8$.

The probability of first ball is red and second ball is blue is

$$\begin{gathered} =\frac{3}{8}\times \frac{5}{7} \\ =\frac{15}{56} \end{gathered}$$

Step: 2 Calculate the probability of first ball is blue and second ball is blue.

There are $3$ red and $5$ blue balls in the urn.

Therefore, total balls in that urn is $8$.

The probability of first ball is red and second ball is blue is

$$\begin{gathered} =\frac{5}{8}\times \frac{4}{7} \\ =\frac{20}{56} \end{gathered}$$

Step: 3 Calculate the required probability.

Therefore, the probability that two balls are drawn in which 2nd ball drawn is blue without replacement is
$$\begin{gathered} =\frac{15}{56}+\frac{20}{56} \\ =\frac{35}{56} \\ =\frac{5}{8} \end{gathered}$$

Therefore, Option(C) is the correct answer.