A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are…

2023

A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is

  1. A.

    7/19

  2. B.

    6/19

  3. C.

    5/19

  4. D.

    4/89

Attempted by 1 students.

Show answer & explanation

Correct answer: A

The correct answer is Option A: 7/19.

Step-by-Step Solution

  1. Understand the Total Combinations: There are 20 bulbs in total, and we are choosing 2. The total number of ways to choose 2 bulbs from 20 is calculated using the combination formula C(n, r) = n! / (r! * (n - r)!).

    • Total cases = C(20, 2) = (20 * 19) / (2 * 1) = 190.

  2. Calculate the Probability of No Defective Bulbs: It is easier to find the probability of choosing zero defective bulbs and subtract that from 1. There are 20 - 4 = 16 non-defective bulbs.

    • Ways to choose 2 non-defective bulbs = C(16, 2) = (16 * 15) / (2 * 1) = 120.

    • Probability of no defective bulbs = 120 / 190 = 12 / 19.

  3. Find the Probability of at Least One Defective Bulb: Subtract the probability of choosing no defective bulbs from the total probability (which is 1).

    • Probability = 1 - (12 / 19)

    • Probability = (19 / 19) - (12 / 19) = 7 / 19.

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