Question 15 - CBSE Class 12 Sample Paper for 2021 Boards

Last updated at Oct. 27, 2020 by Teachoo

The probabilities of A and B solving a problem independently are 1/3 ๐๐๐ 1/4 respectively. If both of them try to solve the problem independently, what is the probability that the problem is solved?

Note
: This
is similar
to
Ex 13.2, 14
of NCERT –
Chapter 13 Class 12 Probability

Question 15 The probabilities of A and B solving a problem independently are 1/3 ๐๐๐ 1/4 respectively. If both of them try to solve the problem independently, what is the probability that the problem is solved?
Given,
P(A) = 1/3 & P(B) = 1/4
Probability that the problem is solved
= Probability that A solves the problem or B solves the problem
= P(A โช B)
= P(A) + P(B) โ P(A โฉ B)
Since A & B are independent,
P(A โฉ B) = P(A) . P(B)
= 1/3 ร 1/4 = 1/12
Now,
P(Problem is solved) = P(A) + P(B) โ P(A โฉ B)
= 1/3 + 1/4 โ 1/12
= 4/12 + 3/12 โ 1/12
= 6/12
= ๐/๐

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.