CBSE Class 12 Mathematics Probability Assignment Set 06

Practice Questions with Answers

Question 1. If A and B are two events such that \( P(A) = \frac{3}{8},\ P(B) = \frac{5}{8} \) and \( P(A \cup B) = \frac{3}{4} \), then find P(A/B) . P(A′/B).
Answer:
\( \frac{6}{25} \)

Question 2. Two events E and F are independent. If P(E) = 0.3 and P(E ∪ F) = 0.5, then find P(E/F) − P(F/E).
Answer:
\( \frac{1}{70} \)

Question 3. If a die is thrown and a card is selected at random from a deck of 52 playing cards, then find the probability of getting an even number on the die and a spade card.
Answer:
\( \frac{1}{8} \)

Question 4. Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, then find the probability of getting a sum 3.
Answer:
\( \frac{1}{5} \)

Question 5. If A and B are two events such that \( P(A) = \frac{1}{2},\ P(B) = \frac{1}{3} \) and \( P(A/B) = \frac{1}{4} \), then find P(A′ ∩ B′).
Answer:
\( \frac{1}{4} \)

Question 6. If A and B are two events such that P(A) = 0.4, P(B) = 0.3 and P(A ∪ B) = 0.5, then find P(B′ ∩ A).
Answer:
\( \frac{1}{5} \)

Question 7. Three persons A, B and C fire at a target in turn, starting with A. Their probabilities of hitting the target are 0.4, 0.3 and 0.2, respectively. Find the probability of two hits.
Answer:
0.188

Question 8. If A and B are two events such that P(A/B) = P(A) = p, \( P(B) = \frac{1}{3} \) and \( P(A \cup B) = \frac{5}{9} \), then find the value of p.
Answer:
\( \frac{1}{3} \)

Question 9. If A and B are such that \( P(A' \cup B') = \frac{2}{3} \) and \( P(A \cup B) = \frac{5}{9} \), then find the value of P(A′) + P(B′).
Answer:
\( \frac{10}{9} \)

Question 10. Let A and B be two events. If P(A/B) = P(A), state whether A and B are independent.
Answer:
Independent

Question 11. The probability that at least one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate P(A′) + P(B′).
Answer:
1.1

Question 12. Three dice are thrown at the same time. Find the probability of getting three 2's, if it is known that the sum of the numbers on the dice was six.
Answer:
\( \frac{1}{10} \)

Question 13. A box has 5 blue and 4 red balls. One ball is drawn at random and not replaced. Its colour is also noted. Then, another ball is drawn at random. What is the probability of the second ball being blue?
Answer:
\( \frac{5}{9} \)

Question 14. A and B throw a pair of dice alternately. A wins the game if he gets a total of 6 and B wins if he gets a total of 7. If A starts the game, then find the probability of A winning the game in the third throw of the pair of dice.
Answer:
\( \frac{775}{7776} \)