There are three boxes, each containing a different number of light

Question

There are three boxes, each containing a different number of light bulbs. The first box has 10 bulbs, of which four are dead, the second has six bulbs, of which one is dead, and the third box has eight bulbs of which three are dead. What is the probability of a dead bulb being selected when a bulb is chosen at random from one of the three boxes?

(A) \(\frac{113}{360}\)

(B) \(\frac{19}{40}\)

(C) \(\frac{13}{24}\)

(D) \(\frac{13}{15}\)

(E) \(\frac{9}{10}\)

(A)  \frac{113}{360}

(B)  \frac{19}{40}

(C)  \frac{13}{24}

(D)  \frac{13}{15}

(E)  \frac{9}{10}

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gmatophobia · Answer

The probability of selecting a dead bulb is = Probability of selecting each box * Probability of selecting a dead bulb from that box

There are three boxes, hence the probability of selecting each box =  \frac{1}{3}

Once a box is selected, the probability of selecting the dead bulb will depend on the selected box.

If the box selected is the one that contains 10 bulbs, the probability of selecting a dead bulb =  \frac{4}{10}  
 If the box selected is the one that contains 6 bulbs, the probability of selecting a dead bulb =  \frac{1}{6}  
 If the box selected is the one that contains 8 bulbs, the probability of selecting a dead bulb =  \frac{3}{8}

Probability of selecting a dead bulb once the box has been identified =  \frac{4}{10} + \frac{1}{6} + \frac{3}{8}

The probability of selecting a dead bulb is =  \frac{1}{3} * (\frac{4}{10} + \frac{1}{6} + \frac{3}{8})

=  \frac{113}{360}

Option A

prachisaraf · Answer

I used (3C1) to select one out of 3 boxes and then choose 1 bulb from that box. So, each case was multiplied by 3 instead of 1/3. What am I missing here ?

szcz · Answer

If you multiply each by 3 then that is the total number of cases. Hence you need to choose one from among those cases. This will give you the probability of 1/3 for selecting boxes which you can multiply by each case.

bumpbot · Answer

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There are three boxes, each containing a different number of light

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There are three boxes, each containing a different number of light

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