Question

of 1000 bolts in a box,20 are defective. find the probability of picking
a) a defective bolt.
b) a good bolt

Answer 1

• The probability of picking a defective bolt = 1/50

• The probability of picking a good bolt = 49/50

Given :

1000 bolts in a box , 20 are defective

To find :

• The probability of picking a defective bolt

• The probability of picking a good bolt

Solution :

Solution :Step 1 of 3 :

Find total number of possible outcomes

There are 1000 bolts in the box

So total number of possible outcomes = 1000

Step 2 of 3 :

Find the probability of picking a defective bolt

Let A be the event that of picking a defective bolt

Since there are 20 defective bolts in the box

So total number of possible outcomes for the event A is 20

Hence the probability of picking a defective bolt

= P(A)

$\displaystyle \sf{ = \frac{Number \: of \: favourable \: cases \: to \: the \: event \: A }{Total \: number \: of \: possible \: outcomes }}$

$\displaystyle \sf{ = \frac{20}{1000} }$

$\displaystyle \sf{ = \frac{1}{50} }$

Step 3 of 3 :

Find the probability of picking a good bolt

The probability of picking a good bolt

= The probability of not picking a defective bolt

$\displaystyle \sf = P( \bar{A})$

$\displaystyle \sf = 1 - P(A)$

$\displaystyle \sf = 1 - \frac{1}{50}$

$\displaystyle \sf = \frac{50 - 1}{50}$

$\displaystyle \sf = \frac{49}{50}$

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