Question

A box of 10 flashbulbs contains 2 defective bulbs. A random sample of 2 is selected and tested. Let x be the random variable associated with the number of defective bulbs in the samplea. find the probability distribution of Xb. find the expected number of defective bulbs in a sample

Answer 1

Step-by-step explanation:

The probability of selecting no bad ones is the probability of

selecting 2 from the 8 good bulbs, which is C(8,2)/C(10,2) or it can also be written as  (8C2)/(10C2) = 28/45

The probability of selecting 1 good one and one bad one, is the

probability of selecting 1 from the 8 good bulbs, and one from

the 2 bad ones, which is [C(8,1)C(2,1)]/C(10,2) or as some people

write it (8C1×2C1)/(10C2) = 16/45.

The probability of selecting two bad one, is C(2,2)/C(10,2) or

as some people write it (2C2)/(10C2) = 1/45.