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
• B. not mutually exclusive but independent events
• C. mutually exclusive and not independent events
• D. neither mutually exclusive nor independent events

Answer 1

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 $P(A\cap B)=\frac{1}{52}$ since ther is only $1$ ace of spades

& $P\left(A\right)P\left(B\right)=\frac{13}{52}\times \frac{4}{52}=\frac{1}{52}$

$P(A\cap B)=P\left(A\right)P\left(B\right)\Rightarrow$ Independent events

$\Rightarrow$ A & B are not mutually exclusive

but independent.