Question 15 - CBSE Class 12 Sample Paper for 2021 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

The probabilities of A and B solving a problem independently are 1/3 𝑎𝑛𝑑 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 𝑎𝑛𝑑 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 ∪ B)
= P(A) + P(B) – P(A ∩ B)
Since A & B are independent,
P(A ∩ B) = P(A) . P(B)
= 1/3 × 1/4 = 1/12
Now,
P(Problem is solved) = P(A) + P(B) – P(A ∩ B)
= 1/3 + 1/4 – 1/12
= 4/12 + 3/12 – 1/12
= 6/12
= 𝟏/𝟐

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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