Question

Here is a table showing all

52

cards in a standard deck.

												Face cards
Color	Suit	Ace	Two	Three	Four	Five	Six	Seven	Eight	Nine	Ten	Jack	Queen	King
Red	Hearts	A ♥	2 ♥	3 ♥	4 ♥	5 ♥	6 ♥	7 ♥	8 ♥	9 ♥	10 ♥	J ♥	Q ♥	K ♥
Red	Diamonds	A ♦	2 ♦	3 ♦	4 ♦	5 ♦	6 ♦	7 ♦	8 ♦	9 ♦	10 ♦	J ♦	Q ♦	K ♦
Black	Spades	A ♠	2 ♠	3 ♠	4 ♠	5 ♠	6 ♠	7 ♠	8 ♠	9 ♠	10 ♠	J ♠	Q ♠	K ♠
Black	Clubs	A ♣	2 ♣	3 ♣	4 ♣	5 ♣	6 ♣	7 ♣	8 ♣	9 ♣	10 ♣	J ♣	Q ♣	K ♣

A five-card hand is dealt at random from a standard deck. (A five-card hand is any set of five different cards, chosen without replacement.)

What is the probability that the hand contains exactly two red cards?

Round your answer to the nearest hundredth.

Answer 1

In general , Probability of an Event =

So Probability that the hand contains exactly two red cards = P(A)  

  

No .of ways to select 'r' no. of objects out of 'n' different objects =

Total no. of ways to select five cards out of 52 cards = = 2598960

No. of ways to select 5 cards such that 2 are red = No. of ways to select 2 red card and 3 non red cards

Using Fundamental Principle of Counting : if there are 'n' no. of ways to do an action and 'm' no. of ways to do another action , then no. of ways to do both actions together = n*m

So,

No. of ways to select 2 red card and 3 non red cards

=( No. of ways to select 2 red card out of 26 red cards) * (No. of ways to select 3 black cards out of 26 black cards)

So Probability that the hand contains exactly two red cards =