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A speaks the truth 3 out of 4 times, and B 5 out of 6 times, what is the probability that they will contradict each other in stating the same fact?

A speaks the truth 3 out of 4 times, and B 5 out of 6 times, what is the probability that they will contradict each other in stating the same fact? Correct Answer 1/3

Given:

A speaks the truth 3 out of 4 times

B speaks the truth 5 out of 6 times

Formula:

Probability = Number of a favorable outcome/Total number of outcomes

P = n(E)/n(S)

Calculation:

Probability that A speak truth P (A) = 3/4

⇒ Probability that A tell a lie P (A) = 1 – ¾ = 1/4

Probability that B speak truth P (B) = 5/6

⇒ Probability that B tell a lie P (B) = 1 – 5/6 = 1/6

The probability that they will contradict each other in stating the same fact

= P (A) × P (B – lie) + P (B) × P (A – lie)

⇒ 3/4 × 1/6 + 5/6 × 1/4

⇒ 1/8 + 5/24

⇒ (3 + 5)/24

⇒ 8/24

⇒ 1/3

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