Question

1. A deck of 52 cards is given. Let the following be events associated with the experiments. A is the event that heart is drawn B is the event that king is drawn (a)Describe the sample space for this experiment. (b)Find the probability of: 1. A 2. B 3. A and B 4. A or C 5. A or B 6. (A|B) 7. Are A and B independent?

Answer 1

a) Sample space for Event A ={A, 2, 3, 4, 5 , 6, 7 ,8 ,9 ,10 ,J ,Q ,K} all card are of hearts

Sample space for Event B ={K_hearts, K_diamond, K_spade, K_club}

b) 1. Probability that heart is drawn, P(A) = 13/52

2. Probability that a king is drawn, P(B) = 4/52

3. Probability of a heart and king, P(A and B) = 1/52 ( because there is only 1 king of hearts)

4. P(A or C) ----- the event C is not defined

5. Probability of a heart or a king, P(A or B) = P(A) + P(B) - P(A and B)

= 13/52 +4/52 - 1/52 = 16/52

6. Probability of A when event B has already happened, P(A|B)= P(A and B)/ P(B)

= (1/ 52) / (4/52) = 1/4

7. no, they are not independent. for independent events P(X and Y)= 0. but that is not true in this case.