# Calculate probability of the event: a randomly selected lamp was produced in the first factory

Problem description:
Only two factories produce lamps of a certain type.
Among the products of the first factory, 2% lamps are defective lamps, among the products of the second - 3%.
It is known that with a randomly selected lamp, the probability of buying a bad lamp of this type is 0.024.
Find the probability that a randomly selected lamp was produced in the first factory.

Problem solution:
Let P be the probability that the lamp was made by the first factory.
Then the probability that the lamp is made in the second factory is 1- P.
The probability the lamp is made in the first factory and at the same time is defective equals to 0.02 × P.
Similarly, the probability that the lamp is made in the second factory and at the same time is bad is 0.03 × (1- P).
Since the probability of buying a faulty lamp is 0.024, according to the formula for adding probabilities, we get the equation:
0.02 × P + 0.03 × (1 - P) = 0.024
Solving this linear equation, we could find: P = 0.6

Answer: the probability a randomly selected lamp is from the first factory is 0.6.

Next probability problem solution: Calculate probability coffee remains in both machines, by the end of the day.

Monday, November 23, 2020
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