Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that one of the cards is a 7 and the other is a 3, and are these events independent?
+118609 Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that one of the cards is a 7 and the other is a 3, and are these events independent?
No they are not independent because the first draw effects the probablility of the second draw.
If the first card WAS replaced then they would be independent.
P(a seven and a 3) = P(7,3) + P(3,7)
=
\(\frac{4}{52}*\frac{4}{51}+\frac{4}{52}*\frac{4}{51}\\ =2*\frac{4}{52}*\frac{4}{51}\\ =\frac{32}{2652}\\ =\frac{8}{663}\)
