Question

A box contains 20 lightbulbs, of which 5 are defective. If 4 lightbulbs are picked from the box randomly, the probability that at most 2 of them are defective is
A. 31/969
B. 70/323
C. 90/323
D. 938/969

Answer 1

Answer:

Option D. 938/969

Step-by-step explanation:

At most 2 defective means 2 or less than 2 bulbs are defective

So, we have 3 cases:

a) No defective bulb.       b) 1 defective bulb.      c) 2 defective bulbs

Case a) No defective bulb

Total number of bulbs = 20

Number of defective bulbs = 5

Number of non-defective bulbs = 15

Total number of ways to select 0 defective bulb = 15C4 = 1365

Case b) 1 defective bulb

Total number of ways to select 1 defective bulb = 15C3 x 5C1 = 2275

Case c) 2 defective bulbs

Total number of ways to select 2 defective bulbs = 15C2 x 5C2 = 1050

Therefore, total number of ways to select at most 2 defective bulbs = 1365 + 2275 + 1050 = 4690

Total number of ways to select 4 bulbs from 20 = 20C4 = 4845

Therefore, probability of selecting at most 2 defective bulbs = $\frac{4690}{4845}=\frac{938}{969}$

Therefore, option D gives the correct answer.