Question

A box contains 4 defective and 2 good parts. Two parts are selected from the box...

A box contains 4 defective and 2 good parts.
Two parts are selected from the box (without replacement), and it is recorded whether the
selected part is defective or good.

The probability that the first selected part is defective and the second selected part is good is
__________

The probability that exactly one good part is selected is__________________

The probability that at least one defective part is selected is _____________________

Sol)

Given

A box contains 4 defective and 2 good parts

Total = 6 parts

Two are selected from the box

a)

Probability that first is defective and second is good

P ( first is defective ) = 4/6

As one is selected is defective in first order

P( second is good ) = 2/5

Total probability = 4C1/6C1 * 2C1/5C1

= 8/30

= 0.26666. = 0.27

b)

Probability that exactly on selected good part

P( one good is selected ) = 8/30 + 8/30

= 16/30

= 0.53333333 = 0.54

c)

Probability that atleast one defective part is selected

P( one is defective ) = (4C1 * 2C1 )/ 6C2

= 8 / 15

P( both are defective ) = 4C2 / 6C2

= 6/15

P(atleast one is defective ) = p( one ) + p( two )

= 8/15 + 6/15

= 14/15

= 0.9333333 = 0.94

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