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A card is drawn at random from a standard deck of cards . Let A be...

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". a) Are A & B mutually exclusive ? b)Are A & B independent ?

Math   Statistics-And-Probability   
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Answer #1

a) Since a card of spade and king exists , hence, A and B can happen at the same time.

Mutually exclusive events cannot happen at the same time.

A and B are not mutually exclusive because A and B can happen at the same time.

b) When two events are said to be independent of each other, what this means is that the probability that one event occurs in no way affects the probability of the other event occurring.

In this case , probability that A occurs in no way affects the probability of the other event B occurring.

Hence, A and B are independent.

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