Exam Questions & Step-by-Step Markschemes (140 Problems)
Question 1 • 2022
2 Marks
Let A and B be two events such that P(A) = \frac{5}{8} , P(B) = \frac{1}{2} and P(A/B) = \frac{3}{4} . Find the value of P(B/A) .
Answer: \frac{3}{5}
Question 2 • 2022
2 Marks
Two balls are drawn at random from a bag containing 2 red balls and 3 blue balls, without replacement. Let the variable X denotes the number of red balls. Find the probability distribution of X.
Answer: X = 0, 1, 2 with P(X) = \frac{3}{10} , \frac{3}{5} , \frac{1}{10}
Question 3 • 2022
4 Marks
A card from a pack of 52 playing cards is lost. From the remaining cards, 2 cards are drawn at random without replacement, and are found to be both aces. Find the probability that lost card being an ace.
Answer: \frac{1}{25}
Question 4 • 2022
4 Marks
A man is known to speak truth 7 out of 10 times. He threw a pair of dice and reports that doublet appeared. Find the probability that it was actually a doublet.
Answer: \frac{7}{22}
Question 5 • 2022
2 Marks
A pair of dice is thrown. It is given that the sum of numbers appearing on both dice is an even number. Find the probability that the number appearing on at least one die is 3.
Answer: \frac{5}{18}
Question 6 • 2022
2 Marks
Probabilities of A and B solving a specific problem are \frac{2}{3} and \frac{3}{5} , respectively. If both of them try independently to solve the problem, then find the probability that the problem is solved.
Answer: \frac{13}{15}