Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. The probability that it was drawn from Bag II is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{35}{68}\)
Let \(E_1\), \(E_2\) be the events that Bag I, Bag II is chosen, each with probability \(\frac{1}{2}\), and R the event that the ball is red:
\( \displaystyle P(R \mid E_1) = \frac{3}{7}, \quad P(R \mid E_2) = \frac{5}{11} \)
By Bayes’ theorem (the common factor \(\frac{1}{2}\) cancels):
\( \displaystyle P(E_2 \mid R) = \frac{\frac{5}{11}}{\frac{3}{7}+\frac{5}{11}} \)
\( \displaystyle = \frac{\frac{35}{77}}{\frac{33+35}{77}} = \frac{35}{68} \)
NCERT (2026-27 edition):
Bayes' Theorem
