Question

A batch of 50 transistors was purchased from different companies A, B and C. 18 of them were manufactured by A, 20 by B and the rest were manufactured by C. The companies A and C produce excellent quality transistors with probability equal to 0.9, B produces the same with the probability equal to 0.6. Then the probability of the event that an excellent quality transistor chosen at random is manufactured by the company B is

Answer 1

Given :  A batch of 50 transistors was purchased from different companies A, B and C. 18 of them were manufactured by A, 20 by B and the rest were manufactured by C.

The companies A and C produce excellent quality transistors with probability equal to 0.9.  B produces the same with the probability equal to 0.6

To Find : probability of the event that an excellent quality transistor chosen at random is manufactured by the company B

Solution:

A = 18

B = 20

C = 50 - 18 - 20 =12

Probability of good Quality from A = 0.9

Hence Expected number of good Quality from A  = 18 * 0.9  = 16.2

Probability of good Quality from B = 0.6

Hence Expected number of good Quality from B  =20 * 0.6  = 12

Probability of good Quality from A = 0.9

Hence Expected number of good Quality from C  =12 * 0.9  = 10.8

Total Expected good Quality = 16.2 + 12 + 10.8  =  39

probability of the event that an excellent quality transistor chosen at random is manufactured by the company B is  = 12/39

= 4/13

4/13 is the  probability of the event that an excellent quality transistor chosen at random is manufactured by the company B  

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