What is the probability, when drawing 5 cards from a fair 52-card deck, of drawing a "full house'' (three of a kind and a pair) in the form AAABB?
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Given:
Cards to be drawn = 5
Total cards = 52
To Find:
Probability of drawing a full house in the form AAABB
Solution:
The probability of drawing in three draws is = 4 / 52 × 3/51 × 2/50 × 13
Where the first of the 3 cards is in a deck with 52 cards, and the second of the 3 cards is in a deck of 51 cards, with the first one removed, then there will be 13 possible cards as three of a kind.
Probability of drawing the pair after three of a kind = 4/49 × 3/48 × 12
= 12/196 = 3/49
Putting it together,
AAABB = 4 / 52 × 3/51 × 2/50 × 13 × 3/49
= 0.00014
Answer: The probability is 0.00014
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