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# a speaks the truth in 70% of cases and b in 90% of the cases. in what percentage of cases are they likely to contradict each other, narrating the same incident?

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## A speaks truth in 70% cases and B in 80% cases. In what percentage of cases they are likely to contradict each other in giving the same statement.

Click here👆to get an answer to your question ✍️ A speaks truth in 70% cases and B in 80% cases. In what percentage of cases they are likely to contradict each other in giving the same statement.

Question

## A speaks truth in 70% cases and B in 80% cases. In what percentage of cases they are likely to contradict each other in giving the same statement.

A

100 38 ​

B

100 62 ​

C

100 72 ​

D

100 18 ​ Medium Open in App Solution Verified by Toppr

Correct option is A)

Let the probability that A and B speak truth be P(A) and P(B) respectively.

Therefore, P(A)= 100 70 ​ = 10 7 ​ and P(B)= 100 80 ​ = 10 8 ​

A and B can contradict in stating a fact when one is speaking the truth and other is not speaking the truth.

Case 1: A is speaking the truth and B is not speaking the truth.

Required probability =P(A)×(1−P(B))=

10 7 ​ ×(1− 10 8 ​ )= 100 14 ​

Case 2: A is not speaking the truth and B is separately the truth.

Required Probability =(1−P(A))×P(B)=(1−

10 7 ​ )× 10 8 ​ = 100 24 ​

Therefore, Percentage of cases in which they are likely to contradict in stating the same fact

=( 100 14 ​ + 100 24 ​ )=( 100 14+24 ​ )= 100 38 ​

141 4

स्रोत : www.toppr.com

## [Solved] Atal speaks the truth in 70% of the cases and George speaks

Concept: P(not A) = 1 - P(A). Probability of a Compound Event [(A and B) or (B and C)] is calculated as: P[(A and B) or (B and C)] = [P(A) × P(B

Home Mathematics Probability Multiplication Theorem of Events

## Atal speaks the truth in 70% of the cases and George speaks the truth in 60% cases. In what percentage of cases are they likely to contradict each other in stating the same fact?

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44% 45% 46% 47%

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## Detailed Solution

Concept:

P(not A) = 1 - P(A).

Probability of a Compound Event [(A and B) or (B and C)] is calculated as:

P[(A and B) or (B and C)] = [P(A) × P(B)] + [P(C) × P(D)]

('and' means '×' and 'or' means '+')

Calculation:

Probability of Atal speaking the truth is 70% = 0.7.

Probability of Atal NOT speaking the truth is 1 - 0.7 = 0.3.

Probability of George speaking the truth is 60% = 0.6.

Probability of George NOT speaking the truth is 1 - 0.6 = 0.4.

They both will contradict each other in the following case:

(Atal speaks the truth AND George does not speak the truth) OR (Atal does not speak the truth AND George speaks the truth).

∴ The required probability is:

[P(Atal speaking the truth) × P(George not speaking the truth)] + [P(Atal not speaking the truth) × P(George speaking the truth)]

= (0.7 × 0.4) + (0.3 × 0.6)

= 0.28 + 0.18 = 0.46.

∴ They both contradict each other in 46% of the cases.

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Last updated on Sep 21, 2022

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स्रोत : testbook.com

## A' speaks truth in 60% cases and 'B' in 70% cases. In what percentages of cases are they likely to contradict each other in stating the same fact?

A' speaks truth in 60% cases and 'B' in 70% cases. In what percentages of cases are they likely to contradict each other in stating the same fact?

Home > English > Class 11 > Maths > Chapter > Probability >

A' speaks truth in 60% cases a...

A' speaks truth in 60% 60% cases and 'B' in 70% 70%

cases. In what percentages of cases are they likely to contradict each other in stating the same fact?

Updated On: 27-06-2022

00 : 15

= 18 100 + 28 100 = 46 100 =18100+28100=46100

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

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