JEE Main · 2024 · 06 Apr 2024 · Shift 1 · Probability

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A company has two plants A and B to manufacture motorcycles. 60% motorcycles are manufactured at plant A and the remaining are manufactured at plant B. 80% of the motorcycles manufactured at plant A are rated of the standard quality, while 90% of the motorcycles manufactured at plant B are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If

p

is the probability that it was manufactured at plant B, then

126 p

(A)64
(B)56
(C)66
(D)54✓ Correct

Answer: (D)

Solution

P (B ∣ S Q) = \frac{P ( B ) P ( S Q ∣ B )}{P ( A ) P ( S Q ∣ A ) + P ( B ) P ( S Q ∣ B )} = \frac{0.4 \times 0.9}{0.6 \times 0.8 + 0.4 \times 0.9} = \frac{0.36}{0.84} = \frac{3}{7} .

126 p = 126 \times \frac{3}{7} = 54.

JEE Main · 2024 · 06 Apr 2024 · Shift 1 · Single correct option

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