Test Index

Probability

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Question : 78 of 127

Marks: +1, -0

Tom speaks truth in 30 percent cases and Dick speaks truth in 25 percent cases. What is the probability that they would contradict each other?

$0.325$
$0.400$
$0.925$
$0.075$

Solution:

Concept:

They contradict when one tells truth and the other lies.

Explanation:

Tom speaks truth in

30\%

cases, so he lies in

70\%

cases.

Dick speaks truth in

25\%

cases, so he lies in

75\%

cases.

Probability that they contradict =

P(\text{Tom truth and Dick lie}) + P(\text{Tom lie and Dick truth})

=

(0.3 \times 0.75) + (0.7 \times 0.25)

=

0.225 + 0.175 = 0.400

Answer:

0.400

which corresponds to option B.

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