Question

Two deck of cards are drawn at random with replacement from a well shuffled pack of 52 cards. Find the probability that the drawn card is a heart and a spade.

Answer 1

Given that:

• Two deck of cards are drawn at random with replacement from a well shuffled pack of 52 cards.

To Find:

• The probability that the drawn card is a heart and a spade.

We know that:

• P(E) = F/T

Where,

• P(E) = Probability of an event
• F = Favourable outcomes
• T = Total outcomes

Finding the favourable outcomes:

• Total number of heart = 13
• Total number of spade = 13

Favorable outcomes = 13 + 13 = 26

Now we have:

• Total outcomes = 52
• Favourable outcomes = 26

Finding the probability that the drawn card is a heart and a spade:

↣ P(E) = 26/52

↣ P(E) = 1/2

Hence,

• The probability that the drawn card is a heart and a spade is 1/2.

Answer 2

Given :-

Two deck of cards are drawn at random with replacement from a well shuffled pack of 52 cards.

To Find :-

Probability that the drawn card is a heart and a spade.

Solution :-

There are two decks. So,

One deck = 52 cards

Two deck = 52 + 52 = 114 cards

Now

Total heart cards = 13 cards

Total spade card = 13 cards

Total card = 13 + 13 = 26 cards

PE = F/T

PE = 26/114

PE = 1/4

Hence

Probability is 1/4 or 0.25