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A box of light bulbs contains exactly 3 light bulbs that are defective. What is the probability that a sample of light bulbs picked at random from this box will contain at least 1 defective light bulb?

Difficulty: 600-700 Level, Probability, Data Sufficiency (DS)

Lunes 25 de julio de 2022, por hurtado claudio

A box of light bulbs contains exactly 3 light bulbs that are defective. What is the probability that a sample of light bulbs picked at random from this box will contain at least 1 defective light bulb?

(1) The light bulbs in the sample will be picked 1 at a time without replacement.
(2) The sample will contain exactly 20 light bulbs.


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EXPLANATION:
Question stem- No.of defective light bulbs are 3.
Total no.of bulbs= unknown

We are asked to find -the probability that a sample of light bulbs picked at random from this box will contain at least 1 defective light bulb.

We need to know total no.of bulbs present in the box and picking methods.

statement 1- Insufficient
Total no.of bulbs not known

Statement 2-insufficient
Picking method not known. We don’t know whether 1 bulb is picked at a time, 2 picked at a time or with/without replacement.

.
Statement 1 + Statement 2

Insufficient.

Reason is we cannot arrive at a unique answer because question stem asks to find probability that atleast 1 defective bulb is picked.
There are 3 cases possible here-
one is defective, 2 defective, 3 are defective. The probability of these 3 cases gives different answer. Hence correct option is E.

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