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Question

A card is drawn from a well shuffled pack of 52 cards. Events A and B are defined as follows :
A : Getting a card of spade
B : Getting an ace, then A and B are .....

A
mutually exclusive and independent events
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B
not mutually exclusive but independent events
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C
mutually exclusive and not independent events
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D
neither mutually exclusive nor independent events
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Solution

The correct option is B not mutually exclusive but independent events
A: Getting a card of spade

B : Getting an ace

i) Events A & B are not mutually exclusive

since the occurrence of one doesn't rule out the occurrence of others. For instance, getting an ace of spade

ii) Events A & B are independent as occurrence

of one is not dependent on other.

also P(AB)=152 since ther is only 1 ace of spades

& P(A)P(B)=1352×452=152

P(AB)=P(A)P(B) Independent events

A & B are not mutually exclusive

but independent.

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