Question

A card is drawn at random from a standard deck of cards. Let A be the event 'card is a spade' and let B be the
event 'card is a king.'
Note: We keep the card back into the deck after drawing.
(a) Are A and B mutually exclusive?
(b) Are A and B independent?
Please select the right set of answers from below:
(a) Yes (b) Yes
(a) Yes (b) No
O(a) No (b) Yes
(a) No (b) No

Answer 1

Answer:

(a) yes (b) yes

hope it will help u....

mark my answer as brain list answer

Answer 2

Answer:

Event A and B are not mutually exclusive. Event A and B are independent.

Therefore, the option (a) No (b)Yes is correct.

Step-by-step explanation:

• The mutually exclusive events are those which cannot occur on same time. For example in a single elevator, you can go either up or down.
• Independent events which do not effect the probabilities of each other.

We have given, Event A : Drawing the card of a Spade

                          Event B : Drawing the card of a King

For event A and B, the card is drawn, can be a king of spade. Therefore, both events can happen at the same time. Therefore, event A and B are not mutually exclusive.

The probability of selected card is spade $=\frac{4}{52}=\frac{1}{13}$

The probability of selected card is King $=\frac{4}{52} =\frac{1}{13}$

The probability of event A could not effect the probability of event B because we put the card back in the deck after drawing it.

Therefore, the event A and B are independent.