Question 5 - Case Based Questions (MCQ) - Chapter 13 Class 12 Probability

Last updated at April 16, 2024 by Teachoo

Question

Anand, Samanyu and Shah of SHORTCUTS classes were given a problem in Mathematics whose respective probabilities of solving it are 1/2, 1/3 and 1/4. They were asked to solve it independently.

Based on the above data, answer any four of the following questions.

Question 1

The probability that Anand alone solves it is _______.

(A) 1/4

(B) 3/4

(C) 11/24

(D) 17/24

Question 2

The probability that problem is not solved is_______.

(A) 1/4

(B) 3/4

(C) 0

(D) 11/24

Question 3

The probability that the problem is solved is _______.

(A) 1/4

(B) 3/4

(C) 17/24

(D) 11/24

Question 4

The probability that exactly one of them solves it is_______.

(A) 1/4

(B) 3/4

(C) 17/24

(D) 11/24

Question 5

The probability that exactly two of them solves it is_______.

(A) 1/4

(B) 3/4

(C) 17/24

(D) 11/24

Transcript

Question Anand, Samanyu and Shah of SHORTCUTS classes were given a problem in Mathematics whose respective probabilities of solving it are 1/2, 1/3 and 1/4. They were asked to solve it independently. Based on the above data, answer any four of the following questions. Let,
A : The event that Anand solves
B : The event that Samanyu solves
C : The event that Shah solves
Given
P(A) = 𝟏/𝟐
P(B) = 𝟏/𝟑
P(C) = 𝟏/𝟒
Question 1 The probability that Anand alone solves it is _______. (A) 1/4 (B) 3/4 (C) 11/24 (D) 17/24 P( A solves alone) = P(A solves)
× P(B does not solve)
× P(C does not solve)
= 1/2×(1−1/3)×(1−1/4)
= 1/2×2/3×3/4
= 𝟏/𝟒
So, the correct answer is (a)
Question 2 The probability that problem is not solved is_______. (A) 1/4 (B) 3/4 (C) 0 (D) 11/24 P(problem is not solved) = P(A does not solve)
× P(B does not solve)
× P(C does not solve)
= (1−1/2)×(1−1/3)×(1−1/4)
= 1/2×2/3×3/4
= 𝟏/𝟒
So, the correct answer is (a)
Question 3 The probability that the problem is solved is _______. (A) 1/4 (B) 3/4 (C) 17/24 (D) 11/24 P(problem is solved) = 1− P(problem is not solved)
= 1 − 1/4
= 𝟑/𝟒
So, the correct answer is (b)
Question 4 The probability that exactly one of them solves it is_______. (A) 1/4 (B) 3/4 (C) 17/24 (D) 11/24
P(exactly one of them solves)
= P(A will solve) × P(B will not solve) × P(C will not solve)
+ P (A will not solve) × P (B will solve) × P (C will not solve)
+ P (A will not solve)× P (B will not solve) × P (C will solve)
= 1/2×(1−1/3)×(1−1/4)
+(1−1/2)×1/3×(1−1/4)
+(1−1/2)×(1−1/3)×1/4
= 1/2×2/3×3/4
+1/2×1/3×3/4
+1/2×2/3×1/4
= 1/4+1/8+1/12
= 𝟏𝟏/𝟐𝟒
So, the correct answer is (d)
Question 5 The probability that exactly two of them solves it is_______. (A) 1/4 (B) 3/4 (C) 17/24 (D) 11/24 P(exactly two of them solves)
= P(A will solve) × P(B will solve) × P(C will not solve)
+ P (A will not solve) × P (B will solve) × P (C will solve)
+ P (A will solve)× P (B will not solve) × P (C will solve)
= 1/2×1/3×(1−1/4)
+(1−1/2)×1/3×1/4
+1/2×(1−1/3)×1/4
= 1/2×1/3×3/4
+1/2×1/3×1/4 +1/2×2/3×1/4
= 1/8+1/24+1/12
= 6/24
= 𝟏/𝟒
So, the correct answer is (a)

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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