lgbasallote
  • lgbasallote
Three cards are given to you from a well-shuffled deck of cards. What is the probability that you get all 3 cards from the same suit?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
thirteen choose three over fifty two choose three
anonymous
  • anonymous
times four
lgbasallote
  • lgbasallote
is this \[\frac 1{52 C3}\]

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KingGeorge
  • KingGeorge
Try the method I was talking about a little earlier.
KingGeorge
  • KingGeorge
You first need to find the possible ways you can choose three cards from the same suit, and then divide by all the possible three card hands. So you have Construction: Choices: 1. Choose a suit \(\binom41\) and then 2. Choose a 3 card set from 13 \(\binom{13}{3}\) So there are \[\binom41\cdot\binom{13}{3}\]3card hands where all the cards are from the same suit.
lgbasallote
  • lgbasallote
so the probability would be \[\frac 1{4 C 1 \times 13 C 3}\]
KingGeorge
  • KingGeorge
Now we need to find all 3 card hands total. This is just \(\binom{52}{3}\) (it's a one step process with how I was doing it before). Thus, your probability would be \[\Large P=\frac{\binom{4}{1}\cdot\binom{13}{3}}{\binom{52}{3}}\]
lgbasallote
  • lgbasallote
probability is.... the possible events over the total right?
KingGeorge
  • KingGeorge
We have to divide by the total number of hands to find probability.
KingGeorge
  • KingGeorge
Right.
lgbasallote
  • lgbasallote
oh. i get the logic now
lgbasallote
  • lgbasallote
thanks
KingGeorge
  • KingGeorge
You're welcome.

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