Question

A box of 500 electric bulbs contains 25 defective bulbs. One bulb is taken out of random from this box. The probability that it is non defective bulbs​

Answer 1

Given,

Total number of electric bulbs in a box = 500

Number of defective bulbs = 25

To find,

If one bulb is taken out of randomly, then the probability that it is a non-defective bulb.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

The probability of occurrence of a favorable event = P (favorable event)

= (Total number of occurrence of the favorable event) / (Total number of occurrence of all possible events)

= (Total number of occurrence of the favorable event) / (Total number of trials)

Now, according to the question;

Total number of bulbs in the box

= (number of defective bulbs) + (number of non-defective bulbs)

=> number of non-defective bulbs = (total number of bulbs in the box) - (number of defective bulbs)

= 500 - 25 = 475

=> number of non-defective bulbs in the box = 475

As per the given question;

The favorable event is the occurrence of a non-defective bulb.

So, the frequency of occurrence of the favorable event = number of non-defective bulbs = 474

And, the total number of trials = total number of bulbs in the box = 500

Now, according to the question;

The probability that a bulb taken out of the box randomly is the non-defective bulb

= (Total number of occurrence of the favorable event) / (Total number of trials)

= (number of non-defective bulbs in the box)/(total number of bulbs in the box)

= 475/500

= 0.95

Hence, the probability that a bulb taken out of the box randomly is non-defective bulb is equal to 0.95.

Answer 2

The probability of choosing non defective bulb is 19/20

Given :

• A box of 500 electric bulbs contains 25 defective bulbs.

• One bulb is taken out of random from this box

To find :

The probability of choosing non defective bulb

Solution :

Step 1 of 3 :

Find total number of possible outcomes

Here it is given that the box has 500 electric bulbs

So total number of possible outcomes = 500

Step 2 of 3 :

Find total number of possible outcomes for the event

Let A be the event that of choosing non defective bulb

Total number of defective bulbs = 25

Total number of non defective bulbs

= 500 - 25

= 475

So total number of possible outcomes for the event A is 475

Step 3 of 3 :

Find the probability

Hence the required probability

= P(A)

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

$\displaystyle \sf{ = \frac{475}{500} }$

$\displaystyle \sf{ = \frac{19}{20} }$

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