Question

Two cards are selected at random from a standard 52-card deck without replacement. Find the probability the first card is the 7 of Diamonds (♦) and the second card is a Club (♣).

Give your answer as a decimal rounded to 4 decimal places

Answer 1

Solution :

Two cards are selected at random

We have to find :

P( First card is 7 numbered Diamond then a club) = P( 7 numbered Diamond) X P( A Club Card)

There is only one card in the deck which is 7 numbered and of Diamond , therefore

P( 7 numbered Diamond) = 1/52

After first card selected, now we have 51 cards left in the deck

There are total 13 cards of club, therefore

P( A club card) = 13/51

Hence

P(First card is 7 numbered Diamond then a club ) =

Answer: The probability the first card is the 7 of Diamonds (♦) and the second card is a Club (♣) is 0.0049