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Chapter 1: Problem 3

Suppose we are playing draw poker. We are dealt (from a well-shuffled deck) five cards, which contain four spades and another card of a different suit. We decide to discard the card of a different suit and draw one card from the remaining cards to complete a flush in spades (all five cards spades). Determine the probability of completing the flush.

Short Answer

Expert verified
The probability of pulling a spade to complete a flush is \(\frac{9}{47}\).

Step by step solution

01

Calculate the Total and remaining number of cards

A standard deck of cards consists of 52 cards - 13 for each suit: spades, clubs, hearts, and diamonds. The player is dealt 5 cards, so before drawing a new card, there are 52 - 5 = 47 cards left in the deck.
02

Calculate the Total and remaining number of spades

The deck has 13 spades, and the player has been dealt with 4 of those. So, there are 13 - 4 = 9 spades left in the deck.
03

Calculate the Probability

Probability (\(P\)) of drawing a spade to complete the flush is found by dividing the number of successful outcomes (i.e., drawing a spade) by the total number of outcomes (i.e., the total number of cards left in the deck). Hence, \(P\) = number of spades left / number of cards left = 9 / 47.

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