Solve the following: In a factory which manufactures bulbs, machines A, B and C manufacture respectively 25%, 35% and 40% of the bulbs. Of their outputs, 5, 4 and 2 percent are respectively defective - Mathematics and Statistics

Sum

Solve the following:

In a factory which manufactures bulbs, machines A, B and C manufacture respectively 25%, 35% and 40% of the bulbs. Of their outputs, 5, 4 and 2 percent are respectively defective bulbs. A bulbs is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by the machine B?

Solution

Let E1, E2, E3 be the events that bulb is manufactured by machines A, B, C respectively.

E1, E2, E3 are mutually exclusive and exhaustive.

It is given that,

P(E1) = 25% = 25/100, P(E2) = 35% = 35/100, P(E3) = 40% = 40/100

Let D ≡ the event that bulb is defective.

It is given that machines A, B, C have outputs of which 5% 4%, 2% are defective,

∴ "P"("D"/"E"_1) = 5/100, "P"("D"/"E"_2) = 4/100, "P"("D"/"E"_3) = 2/100

By Baye's Theorem, the required probability = "P"("E"_2/"D")

= ("P"("E"_2)*"P"("D"/"E"_2))/("P"("E"_1)*"P"("D"/"E"_1) + "P"("E"_2)*"P"("D"/"E"_2) + "P"("E"_3)*"P"("D"/"E"_3))

= ((35/100)*(4/100))/((25/100)*(5/100) + (35/100)*(4/100) + (40/100)*(2/100))

= 140/(125 + 140 + 80)

= 140/345

= 28/69.

Concept: Baye'S Theorem
Is there an error in this question or solution?

APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 9 Probability
Miscellaneous Exercise 9 | Q II. (22) | Page 215