Question

Determine whether the events A and B are independent. Find the probability of event {A and B). Round your answer to 5 decimal places when necessary A card is selected at random from a standard deck of 52 cards. It is then replaced and a second card is selected at random. Event A: A king is selected on the first draw Event B: An ace is selected on the second draw independent A. 0.00592 dependant B. 0.01923 dependant C. 0.02324 independent D. 0.0625 QUESTION 11 Decide whether events A and B are overlapping or non-overlapping. Two die are rolled. Event A: doubles are rolled Event B: 5 is rolled on first dice O A. Overlapping B. Non-overlapping

Answer 1

*) Since, here the card is replaced after 1st draw. So, events are independent.

Event A: there are 4 kings in 52 card deck.

So, the probability of draw 1 king is p(A)=4/52=1/13.

Event B: there are 4 ace in 52 card deck.

So, the probability of draw 1 ace is P(B)=4/52=1/13.

Since events A,B are independent, so P(A and B)=P(A).P(B)=(1/13).(1/13)=1/169=0.00592

**)Two die are rolled.

Event A: double are rolled.so, it contains (1,1), (2,2),(3,3),(4,4),(5,5),(6,6).

Event B: 5 is rolled in first dice. So, it contain (5,1),(5,2),(5,3),(5,4),(5,5),(5,6).

Here, (5,5) is common in both events. So the events are overlapping.