The probability of randomly choosing 3 defectless bulbs from 15 electric bulbs of which 5 bulbs are defective, is :a)3/10b)7/10c)24/91d)67/91Correct answer is option 'C'. Can you explain this answer?

Question

Answer

To find the probability of randomly choosing 3 defectless bulbs from 15 electric bulbs, we can use the concept of combinations.

Step 1: Determine the total number of ways to select 3 bulbs out of 15.
This can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of objects and r is the number of objects to be chosen.

In this case, we want to select 3 bulbs out of 15, so n = 15 and r = 3.
Plugging these values into the formula, we get:
C(15, 3) = 15! / (3!(15-3)!) = 15! / (3!12!) = (15 * 14 * 13) / (3 * 2 * 1) = 455

Therefore, there are 455 different ways to select 3 bulbs out of the 15 available.

Step 2: Determine the total number of ways to select 3 defectless bulbs out of the 10 non-defective bulbs.
Out of the 15 bulbs, 5 are defective, so we have 10 non-defective bulbs to choose from.

Using the same combination formula, we can calculate the number of ways to select 3 bulbs out of 10:
C(10, 3) = 10! / (3!(10-3)!) = 10! / (3!7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

Therefore, there are 120 different ways to select 3 defectless bulbs out of the 10 non-defective bulbs.

Step 3: Determine the probability of selecting 3 defectless bulbs.
The probability of selecting 3 defectless bulbs can be calculated by dividing the number of favorable outcomes (i.e., selecting 3 defectless bulbs) by the total number of possible outcomes (i.e., selecting any 3 bulbs).

The number of favorable outcomes is 120 (from step 2) and the total number of possible outcomes is 455 (from step 1).

Therefore, the probability is:
P = favorable outcomes / total outcomes = 120 / 455 = 24/91

Hence, the correct answer is option C) 24/91.

Answer

Probability required

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