Probability addicts

Probability Level 3

Suppose you are playing a game of Hold'em Poker alone . You are holding 2 Spades in your hand and on the table are other 2 Spades and 1 Diamond. What is the probability of drawing another Spade in 2 tries from your deck?

Details and Assumptions

A deck of cards contains 52 cards (total)
There are 13 spades/diamonds/clubs/hearts in a deck of cards
Answer is up to 4 decimal places (0.abcd)

The answer is 0.3496.

1 solution

Radinoiu Damian
Jul 11, 2015

This is supposed to be a hypergeometric distribution problem (probability without replacement). Let:

$N = 52-5 = 47$
$k = 13-4=9$
$n = 2$
$x \geqslant 1$

All we have to do is calculate $h(x, N, n, k)$ which translates to $h(x\geqslant1, 47, 2, 9) = h(1, 47, 2, 9) + h(2, 47, 2, 9) = \frac{\left(\!\begin{array}{c}9\\1\end{array}\!\right) *\left(\!\begin{array}{c}38\\1\end{array}\!\right)} {\left(\!\begin{array}{c}47\\2\end{array}\!\right)} +\frac{\left(\!\begin{array}{c}9\\2\end{array}\!\right) *\left(\!\begin{array}{c}38\\0\end{array}\!\right)} {\left(\!\begin{array}{c}47\\2\end{array}\!\right)} = 0.3496$

Probability addicts

The answer is 0.3496.

1 solution

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