Question

Consider a well shuffled deck of cards, from which 5 cards are drawn.

a. Find the probability that you get three cards of hearts, and two cards of spades.

b. Find the probability that you get three cards of the same suit, and two cards with the same suit (but different than the one of the three other cards).

Answer 1

A deck of cards has 52 cards. It is given that 5 cards were drawn from a well shuffled deck of cards.

So, number of possible ways to draw

(a)

There are 13 cards in each of the suits like hearts, spreads and two others (diamonds and clubs).

In our favourable case,

• number of ways to choose 3 cards of hearts
• number of ways to choose 2 cards of spades

So, number of favourable cases (choosing 3 cards of hearts and 2 cards of spades)

Hence, required probability of getting three cards of hearts and two cards of spades is given by

(b)

This problem is little bit moderation of previous one and so we may use calculations from previous problem.

Here fixed suit name is not given (as done in earlier part like hearts or spades). So we have to choose suit out of available suits in each step.

So, in our favourable case we get as follows.

• We choose a suit out of 4 suits and choose 3 cards from 13 cards available in that suit. Number of possible ways
• We choose a suit out of remaining 3 suits and choose 2 cards from 13 cards available in that suit. Number of possible ways

So, number of favourable cases (choosing 3 cards from a suit and 2 from another suit)

Hence,required probability of getting three cards from a suit and two cards from another same suit is given by