This unit covers the definition of probability, addition and multiplication theorems, the combination rule, and conditional probability through board-exam numerical questions.
Important Questions
Exam-style questions for this unit (marks shown where available).
1. Intersection from union (2078) [2]
If \(P(A) = 0.6\), \(P(B) = 0.56\) and \(P(A \cup B) = 0.75\), find \(P(A \cap B)\). Where \(A\) and \(B\) are not disjoint events.
2. Scholarship probability and payoff decision (2078)
(a) The probability that a boy will get a scholarship is 0.9 and that a girl will get is 0.8. What is the probability that at least one of them will get the scholarship?
(b) The following table is the conditional payoff table:
| Strategy | N0 (10) | N1 (11) | N2 (12) | N3 (13) | N4 (14) |
|---|---|---|---|---|---|
| S1 (10) | 400 | 400 | 400 | 400 | 400 |
| S1 (11) | 380 | 440 | 440 | 440 | 440 |
| S1 (12) | 360 | 420 | 480 | 480 | 480 |
| S1 (13) | 340 | 400 | 460 | 520 | 520 |
| S1 (14) | 320 | 380 | 440 | 500 | 560 |
What will be your decision if: (i) Maximum criterion is used (ii) Maximum criterion is used (iii) Minimax regret criterion is used?
3. Selection of Ram and Sita (2079) [2]
Ram and Sita appear for an interview for two different posts. The probabilities of their selection are \(\frac{3}{4}\) and \(\frac{1}{5}\) respectively. Find the probability that (a) both of them will be selected (b) none of them will be selected.
4. Drawing a card (2080) [2]
A card is drawn at random from a pack of cards. What is the probability of getting (a) a black card and (b) a king?
5. Intersection from union (2081) [2]
If \(P(A) = 0.6\), \(P(B) = 0.5\) and \(P(A \cup B) = 0.4\), find \(P(A \cap B)\). Where \(A\) and \(B\) are not mutually exclusive events.
6. Ball numbered 1 to 20 — multiple of 4 or 7 (2082) [2]
Twenty balls are numbered from 1 to 20. If one ball is drawn at random, what is the probability that the ball drawn is a multiple of 4 or 7?
7. Ball numbered 1 to 20 — multiple of 3 or 7 (2083) [2]
A bag contains 20 balls numbered from 1 to 20. One ball is drawn at random. Find the probability that the number on the drawn ball is a multiple of 3 or 7.