NIMCET 2013 — Mathematics PYQ

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Question

NIMCET 2013 — Mathematics PYQ

NIMCET | Mathematics | 2013

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?

Choose the correct answer:

Explanation

Solution

Step 1: Identify individual probabilities

Let $A$ be the event that Atal speaks the truth and $G$ be the event that George speaks the truth.

P(A) = \frac{70}{100} = 0.7

P(G) = \frac{60}{100} = 0.6

Step 2: Find the probabilities of lying

P(\text{Atal lies}) = P(A') = 1 - 0.7 = 0.3

P(\text{George lies}) = P(G') = 1 - 0.6 = 0.4

Step 3: Define "Contradiction"

They contradict each other in two cases:

Atal speaks the truth AND George lies.
Atal lies AND George speaks the truth.

P(\text{Contradiction}) = [P(A) \times P(G')] + [P(A') \times P(G)]

Step 4: Calculate the total probability

P(\text{Contradiction}) = (0.7 \times 0.4) + (0.3 \times 0.6)

P(\text{Contradiction}) = 0.28 + 0.18

P(\text{Contradiction}) = 0.46

Step 5: Convert to percentage

\text{Percentage} = 0.46 \times 100 = 46\%

Final Answer:

The likely percentage of contradiction is 46%.

Choose the correct answer:

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