Question

A box consists of 60 wall clocks, out of which 40 are good, 15 have minor defects and the remaining are broken. What is the probability that
(i) the box will be rejected?
(ii) the clock has minor defect?

Hint:

Always reduce your fractions to the simplest form in probability answers to ensure full marks.

Answer 1

Step 1: Understanding the Concept:
Probability is the ratio of favorable outcomes to the total outcomes.
Step 2: Key Data:
Total clocks = 60.
Good = 40.
Minor defect = 15.
Broken = \(60 - (40 + 15) = 5\).
Step 3: Detailed Explanation:
1. Case (i): Box is rejected. The trader rejects the box if the clock taken out is broken.
\[ P(\text{Rejected}) = \frac{\text{Broken Clocks}}{\text{Total Clocks}} = \frac{5}{60} = \frac{1}{12} \] 2. Case (ii): Clock has minor defect.
\[ P(\text{Minor defect}) = \frac{15}{60} = \frac{1}{4} \]
Step 4: Final Answer:
(i) Probability of rejection is \(\frac{1}{12}\). (ii) Probability of minor defect is \(\frac{1}{4}\).