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