Maths · Probability: Probability of an event, addition and multiplication theorems of probability

There are three boxes, each containing a different number of light bulbs. The fi

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. \( \frac{115}{330} \)
  • B. \( \frac{113}{360} \)
  • C. \( \frac{113}{330} \)
  • D. None of these

Step-by-step solution

Probability of selecting a dead bulb = (1/3)*(4/10) + (1/3)*(1/6) + (1/3)*(3/8) = (1/3)*(2/5 + 1/6 + 3/8) = (1/3)*(113/120) = 113/360.
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