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Mathematics · Probability

JEE Main 2024 — 6 April, Shift 1 — Question 10

A company has two plants AA and BB to manufacture motorcycles. 60%60 \% motorcycles are manufactured at plant A and the remaining are manufactured at plant B. 80%80 \% of the motorcycles manufactured at plant A are rated of the standard quality, while 90%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 pp is the probability that it was manufactured at plant BB, then 126 p is

  1. Option A:

    54

    Correct
  2. Option B:

    64

  3. Option C:

    66

  4. Option D:

    56

Answer: A

Step-by-step solution

AB
Manufactured60%40%
Standard quality80%90%

P(\mathrm{P}( Manufactured at B/\mathrm{B} / found standard quality )=)= ?

A : Found S.Q

B : Manufacture B

C : Manufacture A

P(E1)=40100\mathrm{P}\left(\mathrm{E}_{1}\right)=\frac{40}{100}

P(E2)=60100P\left(E_{2}\right)=\frac{60}{100}

P(A/E1)=90100\mathrm{P}\left(\mathrm{A} / \mathrm{E}_{1}\right)=\frac{90}{100}

P(A/E2)=80100\mathrm{P}\left(\mathrm{A} / \mathrm{E}_{2}\right)=\frac{80}{100}

∵P(E1/A)=P(A/E1)P(E1)P(A/E1)P(E1)+P(A/E2)P(E2)=37\because \mathrm{P}\left(\mathrm{E}_{1} / \mathrm{A}\right)=\frac{\mathrm{P}\left(\mathrm{A} / \mathrm{E}_{1}\right) \mathrm{P}\left(\mathrm{E}_{1}\right)}{\mathrm{P}\left(\mathrm{A} / \mathrm{E}_{1}\right) \mathrm{P}\left(\mathrm{E}_{1}\right)+\mathrm{P}\left(\mathrm{A} / \mathrm{E}_{2}\right) \mathrm{P}\left(\mathrm{E}_{2}\right)}=\frac{3}{7}

∴126P=54\therefore 126 \mathrm{P}=54

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Paper
6 April, Shift 1
Subject
Mathematics
Chapter
Probability
Topic
Total Probability and Baye's Theorem

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