Hello,
Greetings for the day!
This is a question of medium difficulty level. The statements have been framed in such a way that if you do not examine them carefully, you will end up falling for the trap answer which is Option C.
Let us now look at how to solve this question:
Of the 20 bulbs, let ‘x’ bulbs be defective and ‘y’ be non-defective.
If 2 bulbs are selected at random, the total possible outcomes will be 20C2.
Now, 20C2 = (20 x 19)/2 = 190.
Number of ways to select two bulbs which are defective = xC2, which also represents the favourable outcomes for the event defined in the question.
Therefore, Probability (Both bulbs are defective) = xC2 /190 The question asks us if this probability is less than 0.4.
Now, 0.4 = 2/5.
Hence, we are trying to ascertain if (xC2 / 190) < (2/5) which simplifies to whether
xC2 < 76.
xC2 can be less than 76 only if x is less than 13. Now, this is the data that we have to look for in the statements.
Statement I says that more than 50% of the bulbs were defective. This means that x can be 11 or higher. This does not conclusively tell us if x is less than 13 or not. Hence, statement I alone is insufficient.
Statement II says that less than 60% of the bulbs are defective. This means that x is 12 or lesser. If x is 12 or lesser, it is definitely lesser than 13, which is what we were trying to ascertain. Hence, statement II alone is sufficient.
Hence, the correct answer option is B.
In such DS questions on probability, it is important to analyse the question as much as possible and create a mathematical situation wherein you can use the data given in the statements with ease, as we did in this question. If you do not utilize the question data to your advantage, you will end up resorting to plugging in values which is not the ideal method for such questions.
Hope this helps!
Cheers.
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- CrackVerbal Prep Team
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