Question

Answer ASAP Probability and Stats

An ordinary deck of 52 cards consists of 4 suits (hearts, diamonds, spades and clubs), each having 13 ranks (2, 3, ...,10, J, Q, K, A). 5 cards are randomly selected from the deck (without replacement). What is the probability that the outcome consists of

(a) 5 hearts, or

(b) 3 diamonds and 2 spades, or

(c) cards from more than one suit.

In this question, there is no need to evaluate your expression to a number.

Answer 1

Total cards = 52

Total number of ways to choose 5 cards out of 52 cards = ⁵²C₅

a) Total heart = 13

P(5 hearts) = ¹³C₅ / ⁵²C₅

b) P(3 diamonds and 2 spades) = ¹³C₃ * ¹³C₂ / ⁵²C₅

c) P(cards from more than one suit) = 1 - P(cards from exactly one suit)

                                                          = 1 - (⁴C₁ * ¹³C₅ / ⁵²C₅)