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. $\dfrac{5}{{16}}$
B. $\dfrac{5}{{56}}$
C. $\dfrac{5}{8}$
D. $\dfrac{{20}}{{56}}$

Answer 1

Hint: There are two cases to solve the equations. First case: the first ball is in red color and the second ball is blue in color. Second case: the first ball is blue in color and the second ball is blue in color. Then add the probability of two cases to get the required solution.

Formula Used:
Required Probability $ = P$ (First ball is red, second ball is blue) $ + P$ (First ball is blue, second ball is blue)

Complete step by step solution:
We have been given that total number of balls $ = 3 + 5 = 8{\rm{ balls}}$
Probability of first ball is red & second ball is blue $ = \dfrac{3}{8} \cdot \dfrac{5}{7}$
Probability of first ball is blue & second ball is blue $ = \dfrac{5}{8} \cdot \dfrac{4}{7}$
Therefore,
Required Probability $ = P$ (First ball is red, second ball is blue) $ + P$ (First ball is blue, second ball is blue)
Required Probability $ = \dfrac{3}{8} \cdot \dfrac{5}{7} + \dfrac{5}{8} \cdot \dfrac{4}{7}$
Hence, the probability that the second ball drawn is red $ = \dfrac{5}{8}$.

Option ‘C’ is correct

Note: We have to use the concept of probability distribution to solve the question which states that probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about how probable an event is to happen, or its likelihood of happening. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty.