Question 12 (Or 1st) - CBSE Class 12 Sample Paper for 2019 Boards

Last updated at Oct. 1, 2019 by Teachoo

Question 12 (OR 1
st
question)
One bag contains 3 red and 5 black balls. Another bag contains 6 red and 4 black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is red.

Question 12 (OR 1st question) One bag contains 3 red and 5 black balls. Another bag contains 6 red and 4 black balls. A ball is transferred from first bag to the second bag and then a ball is drawn from the second bag. Find the probability that the ball drawn is red.
3 Red (R)
5 Black (B)
6 Red (R)
4 Black (B)
Probability that ball drawn is red
= Probability that ball transferred is red
× Probability that red ball is picked from 2nd bag
+ Probability that ball transferred is black
× Probability that red ball is picked from 2nd bag
3 Red (R)
5 Black (B)
6 Red (R)
4 Black (B)
If red ball is transferred
Probability that ball transferred is red = 3/8
Probability of getting a red ball from Bag II = 7/11
If black ball is transferred
Probability that ball transferred is black = 5/8
Probability of getting a red ball from Bag II = 6/11
Thus,
Probability that ball drawn is red = 3/8 × 7/11 + 5/8 × 6/11
= 21/88 + 30/88
= 51/88
Thus, required probability is 𝟓𝟏/𝟖𝟖

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.