A Box Contains 20 Electric Bulbs, Out of Which 4 are Defective GMAT Problem Solving

Question: A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are drawn at random. The probability that atleast one of these are defective:

1. \(\frac{4}{19}\)
2. \(\frac{7}{19}\)
3. \(\frac{12}{19}\)
4. \(\frac{10}{19}\)
5. \(\frac{11}{19}\)

Answer:

Solution with Explanation:
Approach Solution (1):

This actually makes no difference at all. After all, if you put two hands in the box and take hold of the two light bulbs, it won’t be any more or less likely you get two defective bulbs if you take your hands out of the box one at a time than if you take them both out at once.

There problems are much easier by making the selections one at a time. We can then avoid using expressions like \(^{20}C_2\) altogether. If I pick one bulb at a time, the probability the first is defective is \(\frac{16}{20}\), and the probability the second is then also defective is \(\frac{15}{19}\), so the probability both are defective is:

(\(\frac{16}{20}\))(\(\frac{15}{19}\)) = (\(\frac{12}{19}\))

And the probability atleast one is defective is 1 -\(\frac{12}{19}\) = \(\frac{7}{19}\)

Correct Option: B

Approach Solution (2):

We have remember one thing that for all the questions having “atleast” option, try to find the probability in reverse manner.
This means:
P (Probability that atleast one of the bulb is defective) = 1 – P (Probability that none of the bulb is defective)
P (Probability that atleast one of the bulb is defective) = \(1 –(\frac{^{16}C_2}{^{20}C_2}) = \frac{7}{19}\)

Correct Option: B

“A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are drawn at random. The probability that atleast one of these are defective:”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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