A single card id drawn from each of six well shuffled decks of playing card. Let A be the event that all six cards drawn are different.

(a) find P(A)

(b) Find the probability that at least two of the drawn card match.

Please help.

Thanks

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- Feb 6th 2009, 09:11 AMjojo_jojo[SOLVED] probability question
A single card id drawn from each of six well shuffled decks of playing card. Let A be the event that all six cards drawn are different.

(a) find P(A)

(b) Find the probability that at least two of the drawn card match.

Please help.

Thanks - Feb 6th 2009, 09:23 AMPlato
Do we consider $\displaystyle 3\heartsuit,\:3\clubsuit$ as different cards??

- Feb 6th 2009, 09:57 AMSoroban
Hello, jojo_jojo!

Quote:

A single card is drawn from each of six well-shuffled decks of playing cards.

Let $\displaystyle A$ be the event that all six cards drawn are different.

(a) Find $\displaystyle P(A)$

The first card can be any card: .$\displaystyle \frac{52}{52} \,=\,1$

The second can be any of the other 51 cards: .$\displaystyle \frac{51}{52}$

The third can be any of the other 50 crds: .$\displaystyle \frac{50}{52}$

The fourth can be any of the other 49 cards: .$\displaystyle \frac{49}{52}$

The fifth can be any of the other 48 cards: .$\displaystyle \frac{48}{52}$

The sixth can be any of the other 47 cards: .$\displaystyle \frac{47}{52}$

Therefore: .$\displaystyle P(\text{6 different}) \:=\:1\cdot\frac{51}{52}\cdot\frac{50}{52}\cdot\fr ac{49}{52}\cdot\frac{48}{52}\cdot\frac{47}{52} \;\approx\;0.74$

Quote:

(b) Find the probability that at least two of the drawn card match.

The opposite of "no matches" is "at least one match".

$\displaystyle P(\text{at least one match}) \;=\;1-0.74 \;=\;0.26$

- Feb 6th 2009, 10:32 AMjojo_jojoThanks a lot!!
Thanks Soroban :).