Question

A card is drawn from a pack of 52 cards so that each card is equally likely to be drawn from a pack A is the event that the card drawn is of spade and B is the event where the card drawn is an ace explain whether 2 events are independent

Answer 1

Yes the two events are different

Answer 2

Answer:

Yes, the events are independent

Step-by-step explanation:

Two events are said to be independent when,

P ( A ∩ B ) = P ( A ) * P ( B )

Given,

One card is drawn from a pack of 52 cards

According to event A :

The card drawn is a spade

Number of spades in a pack of card = 13

Total number of cards = 52

P ( A ) = $\frac{13}{52}$ = $\frac{1}{4}$

Similarly,

According to event B :

The card drawn is an ace

Number of spades in a pack of card = 4

Total number of cards = 52

P ( B ) = $\frac{4}{52}$ = $\frac{1}{13}$

Now,

A ∩ B : The card drawn is an ace of spades

Number of an ace of spades in pack of card = 1

So,

P ( A ∩ B ) = $\frac{1}{52}$

Now,

P ( A ) * P ( B ) = $\frac{1}{4}$ * $\frac{1}{13}$

P ( A ) * P ( B ) = $\frac{1}{52}$

Since,

P ( A ∩ B ) = P ( A ) * P ( B )

Hence,

2 events A and B are independent