Suppose we are playing draw poker. we are dealt (from a well-shuffled deck) five cards, which contain four spades and another ca

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Suppose we are playing draw poker. we are dealt (from a well-shuffled deck) five cards, which contain four spades and another ca

rd 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.

Mathematics

1 answer:

Leona [12.6K] · Answer 1 · 2026-04-06T01:02:19+03:00

Assuming we start with a full standard deck of 52 and then draw 4 spades along with 1 card from a different suit, that leaves us with 47 cards still in the deck. We are hoping to draw another spade from these remaining cards. Initially, there were 13 spades, but after drawing five cards, 9 spades remain in the deck. The likelihood of pulling one of these 9 spades from the 47 cards is

$\dfrac{\binom91\binom{38}0}{\binom{47}1}=\dfrac9{47}$

In other words, we want to get any 1 of the available 9 spades while avoiding any of the other 38 non-spades, and we're drawing just a single card from the 47 cards total.