Exam Questions & Step-by-Step Markschemes (3 Problems)
Question 1 • 2023
5 Marks
A manufacturing firm has three machines A, B , and C producing bolts. Machine A produces 30\% , machine B produces 45\% , and machine C produces 25\% of the total output. Past experience shows that 2\%, 3\% , and 4\% of the bolts produced by machines A, B , and C respectively are defective. A bolt is drawn at random from the output and is found to be defective. Find the probability that it was manufactured by machine B .
Answer: P(\text{Machine } B \mid \text{Defective}) = \frac{27}{59} \approx 45.76\%
Question 2 • 2023
4 Marks
An unbiased coin is tossed 6 times. Find the probability of getting: (i) Exactly 4 heads. (ii) At least 4 heads.
Answer: (i) \ \frac{15}{64} \quad (ii) \ \frac{11}{32}
Question 3 • 2023
6 Marks
An insurance company insured 2000 scooter drivers, 4000 car drivers, and 6000 truck drivers. The probability of an accident involving a scooter, a car, and a truck driver is 0.01, 0.03, and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a car driver?
Answer: P(E_2|A) = \frac{3}{26}