Choosing a defective product from a lot

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Problem 4

A lot consists of 12 good products, 6 with minor defects and 2 with major defects. A product is chosen at random. The probability that it is defective is
Ans :
2
5

Solution

Total number of products in the lot

= 12 Good + 6 with Minor Defects + 2 With Major Defects

= 20

Experiment :

Choosing a product from the lot

Total Number of Possible Choices

= Number of ways in which a product can be chosen from among the 20 products in the lot

⇒ n = 20C1
=
20
1
= 20

Let

A : the event of choosing a defective product

For Event A

Number of defective products

= 6 with Minor Defects + 2 With Major Defects

= 8

Favorable
(defective) 		Unfavorable
(Others) 		Total
Available 8 12 20
To Choose 1 0 1
Choices 8C122C020C1

Number of Favorable Choices

= Number of ways in which a defective product can be selected from the total 8 favorable products

⇒ mA = 8C1
=
8
1
= 8

Probability of choosing a defective product

⇒ Probability of occurrence of Event A

=
Number of Favorable Choices for the Event
Total Number of Possible Choices for the Experiment
⇒ P(A) =
mA
n
=
8
20
=
2
5

Odds

Number of Unfavorable Choices

= Total Number of possible choices − Number of Favorable choices

⇒ mAc = n − mA
= 20 − 8
= 12

in favor

Odds in Favor of choosing a defective product

⇒ Odds in Favor of Event A

= Number of Favorable Choices : Number of Unfavorable Choices

= mA : mAc

= 8 : 12

= 2 : 3

against

Odds against choosing a defective product

⇒ Odds against Event A

= Number of Unfavorable Choices : Number of Favorable Choices

= mAc : mA

= 12 : 8

= 3 : 2

Author : The Edifier
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