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February 2020 Brain Puzzler Solution

Q: In an economy pack of 12 highlighters, 3 are defective.

If you purchase 2 highlighters (picked randomly), what is the probability that neither highlighter is defective?

A: 6/11
Since there are 3 defective highlighters out of 12, the probability of selecting the first non-defective highlighter is 9/12.
The probability of selecting the second non-defective highlighter is 8/11 as 11 highlighters remain and only 8 of them are good.
Therefore, the probability that a customer buys 2 non-defective highlighters is:
= 9/12 x 8/11
= 3/4 x 8/11
= 24/44
= 6/11.