1. Question 1 Q. Four cards are drawn from a pack of 52 cards. Find the probability of, 1. They are King, Queen, Jack, & Ace 2. First is King, then Queen, then Jack and finally Ace. 3. All are Diamonds 4. Two are red and two are Black

2. Question 2  In a box there are 2 white and 4 black balls. What is the probability that both of the two balls drawn (with & without replacement), one after the other, are White?

3. Question 3  A bag contains 4 white, 5 red, and 6 green balls. Three balls are drawn at random. What is the probability that a white, a red and a green ball is drawn?

4. Question 4  A bag contains 4 white, 5 red, and 6 green balls. Three balls are drawn at random. What is the probability that first is white, second is red and third is green ball?

5. QUESTION 5 A can solve 80% of the problems; B can solve 90% of them. A problem is selected at random. What is the probability that that, i) None of them can solve it. ii) At least one of them solves it. iii) Both of them solve it.

6. Question 6  A speak truth in 60% of cases and B in 75% of cases. In what percentage of cases both are likely to contradict each other in the same fact?

7. Question 7  The probability that A will solve a question is ½, that B can solve is 1/3 and C can solve is 1/5. If all of them try it independently, then find the probability that the problem will be solved.

8. Question 8 Statistical Independence case Marginal probability: It is simply the probability of occurrence of that event. e.g. Tossing of a coin; P(H) = 0.5, and P(T) = 0.5

9. Question 8 Statistical Independence case Joint Probability: It is the probability of occurrence of two or more events simultaneously. In independence case it is the product of their respective marginal probabilities. e.g. Getting Heads in two toss of a coin. P(HH) = ½ * ½ = ¼

10. Question 8 Statistical Independence case Conditional Probability: as per definition, conditional probability of event A, P(A/B) is defined as the probability of happening of A provided B has already occurred. In independence case, P(A/B) = P(A)

11. Question 9 Statistical Dependence case Suppose a bag contains10 balls such as, Three are colored and dotted One is colored and stripped Two are grey and dotted Four are gray and stripped.

12. Question 9 Statistical Dependence case Marginal Probability: Find the probability of colored ball P(C). Joint Probability: Probability that the drawn ball is colored and stripped P(CS). Conditional Probability: Probability of colored ball provided the drawn ball is Stripped P(C/S)

13. Question 9 Statistical Dependence case P(C) = P(D) + P(S) = 0.3+0.1 = 0.4 P(CS) = P(C/S) * P(S) = 0.2 * 0.5 = 0.1 P(C/S) = P(CS) / P(S) = 0.1/ 0.5 = 0.2