# [SOLVED] probability question

• February 6th 2009, 09:11 AM
jojo_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.

Thanks
• February 6th 2009, 09:23 AM
Plato
Do we consider $3\heartsuit,\:3\clubsuit$ as different cards??
• February 6th 2009, 09:57 AM
Soroban
Hello, jojo_jojo!

Quote:

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

(a) Find $P(A)$

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

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

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

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

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

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

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

Quote:

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

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

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

• February 6th 2009, 10:32 AM
jojo_jojo
Thanks a lot!!
Thanks Soroban :).