3 cards are drawn from a standard 52 playing cards deck. Find the odds of drawing just two spades?

amanf 2021-09-08 Answered
3 cards are drawn from a standard 52 playing cards deck. Find the odds of drawing just two spades?

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svartmaleJ
Answered 2021-09-09 Author has 17202 answers
There're 3 ways to draw exactly 2 hearts when 3 cards are drawn:
The 1st and 2nd cards are spades. probability of \(\displaystyle\frac{{13}}{{52}}\times\frac{{12}}{{51}}\times\frac{{39}}{{50}}={0.046}\)
The 1st and 3rd cards are spades. probability of \(\displaystyle\frac{{13}}{{52}}\times\frac{{39}}{{51}}\times\frac{{12}}{{50}}={0.046}\)
The 2nd and 3rd cards are spades. probability of \(\displaystyle\frac{{39}}{{52}}\times\frac{{13}}{{51}}\times\frac{{12}}{{50}}={0.046}\)
The odds of drawing 2 spades are 0.046=4.6%
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