# Thread: [SOLVED] probability question

1. ## [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

2. Do we consider $\displaystyle 3\heartsuit,\:3\clubsuit$ as different cards??

3. Hello, jojo_jojo!

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

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

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

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

4. ## Thanks a lot!!

Thanks Soroban .