Verified Solution • 2025–26 Session moderate

QJEEM24Ma062a: JEE Main 2024 Mathematics - Class 12 JEEM24Ma062a Solution: A company has two plants and to manufacture motorcycles.…

A company has two plants AA and BB to manufacture motorcycles. 60%60 \% motorcycles are manufactured at plant AA and the remaining are manufactured at plant B.80%B .80 \% of the motorcycles manufactured at plant AA are rated of the standard quality, while 90%90 \% of the motorcycles manufactured at plant BB 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 126p126 p is

Multiple Choice Options

  • A 54
  • B 66
  • C 56
  • D 64

Step-by-Step Verified Solution

amp;P( standard automobile from A)=610×810=1225amp;P( standard automobile from B)=410×910=925\begin{aligned}& P(\text { standard automobile from } A)=\frac{6}{10} \times \frac{8}{10}=\frac{12}{25} \\& P(\text { standard automobile from } B)=\frac{4}{10} \times \frac{9}{10}=\frac{9}{25}\end{aligned}

amp; Required Probability 9251225+925amp;P=921=37\begin{aligned}& \text { Required Probability } \frac{\frac{9}{25}}{\frac{12}{25}+\frac{9}{25}} \\& P=\frac{9}{21}=\frac{3}{7}\end{aligned}

So, 126P=126×37=54126 P=126 \times \frac{3}{7}=54

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