Choosing a non defective bolt from a box containg bolts

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Problem 3

A box contains 400 bolts of which 20 are defective. Find the probability that a bolt chosen at random from the box is not defective.

Solution

Total number of bolts

= 400

Experiment :

Choosing a bolt from the 400 bolts in the box

Total Number of Possible Choices

= Number of ways in which a bolt can be chosen from among the 400 bolts in the box

⇒ n = 400C1
=
400
1
= 400

Let

A : the event of choosing a non defective bolt

For Event A

Number of defective bolts

= 20

Number of non defective bolts

= Total number of bolts in the box − Number of defective bolts in the box

= 400 − 20

= 380

Favorable
(non defective) 		Unfavorable
(Others) 		Total
Available 380 20 400
To Choose 1 0 1
Choices 380C120C0400C1

Number of Favorable Choices

= Number of ways in which a non defective bolt can be selected from the total 380 favorable bolts

⇒ mA = 380C1
=
380
1
= 380

Probability of choosing a non defective bolt

⇒ 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
=
380
400
=
19
20

Odds

Number of Unfavorable Choices

= Total Number of possible choices − Number of Favorable choices

⇒ mAc = n − mA
= 88 − 8
= 80

in favor

Odds in Favor of choosing a non defective bolt

⇒ Odds in Favor of Event A

= Number of Favorable Choices : Number of Unfavorable Choices

= mA : mAc

= 380 : 20

= 19 : 1

against

Odds against choosing a non defective bolt

⇒ Odds against Event A

= Number of Unfavorable Choices : Number of Favorable Choices

= mAc : mA

= 20 : 380

= 1 : 19

Author : The Edifier
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