Multiple choice

A garage mechanic keeps a box of good springs to use as replacements on customers cars. The box contains $5$ springs. A colleague, thinking that the springs are for scrap, tosses three faulty springs into the box. The mechanic picks two springs out of the box while servicing a car. Find the probability that the second spring drawn is faulty.

  1. $\dfrac{1}{8}$
  2. $\dfrac{2}{8}$
  3. $\dfrac{3}{8}$
  4. $\dfrac{4}{8}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total springs = 5 + 3 = 8. Good = 5, Faulty = 3. Probability second is faulty = P(1st good, 2nd faulty) + P(1st faulty, 2nd faulty) = (5/8 * 3/7) + (3/8 * 2/7) = 15/56 + 6/56 = 21/56 = 3/8.

AI explanation

Using the law of total probability, the desired probability is the sum of getting a faulty spring on the second draw given the first was good, plus getting a faulty spring given the first was faulty. This is calculated as (5/8 multiplied by 3/7) plus (3/8 multiplied by 2/7), which equals 15/56 plus 6/56. The final sum is 21/56, which simplifies to 3/8.

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