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 is

Solution

Maths sir · 3 steps

Find how much of the standard output comes from plant B, then divide by all the standard output.

1. Set up events. Let S be the event that the motorcycle is of standard quality. Plant A makes 60% of the motorcycles and plant B makes 40%, so P(A) = 0.6 and P(B) = 0.4.

   Plant	Share of production	Standard rate	Standard and from this plant
   A	0.6	0.8	0.6 × 0.8 = 0.48
   B	0.4	0.9	0.4 × 0.9 = 0.36

2. Total standard. By the total probability theorem, P(S) = 0.48 + 0.36 = 0.84. This is the whole pool the chosen motorcycle came from.

   p = P(B | S) = (P(B) P(S | B))/P(S) = 0.36/0.84 = 3/7

3. So. 126p = 126 × 3/7 = 54, which is option (a).

The idea to keep. In Bayes questions, write each source's share times its rate. The required probability is that source's product divided by the sum of all the products.

Answer from the NTA final answer key. Solution by PrepWiser.