Exam Questions & Step-by-Step Markschemes (4 Problems)
Question 1 • 2024
4 Marks
An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The accident probabilities are 0.01, 0.03 and 0.15 respectively. One driver meets with an accident. What is the probability that he is a scooter driver?
Answer: P(E_1|A) = \frac{1}{52}
Question 2 • 2024
4 Marks
Two cards are drawn simultaneously (without replacement) from a well-shuffled pack of 52 cards. Find the mean and variance of the number of red cards.
Answer: \text{Mean } E(X) = 1, \quad \text{Variance } \text{Var}(X) = \frac{9}{17} \approx 0.529
Question 3 • 2023
4 Marks
A die is thrown 6 times. If 'getting an odd number' is a success, what is the probability of: (i) At least 5 successes? (ii) At most 5 successes?
Answer: (i) \ \frac{7}{64} \quad (ii) \ \frac{63}{64}
Question 4 • 2023
4 Marks
Two cards are drawn simultaneously (or successively without replacement) from a well-shuffled pack of 52 cards. Find the mean and variance of the number of red cards.
Answer: \text{Mean } = 1, \quad \text{Variance } = \frac{25}{51}