nonameee wrote:
There are 5 pairs of socks: 2 blue, 2 white, 2 black, 2 yellow, 2 green. You select randomly four socks together. What is the probability that you'll get at least two of the same color?
I think it's
The book says it's
which is in my opinion a mistake.
I think you are right.
"Probability that you'll get at least two of the same color" - means at least one pair (one pair or two pairs out of 4 socks).
P(at least one pair)=1-P(no pair) --> no pair means all socks must be of different colors --> \(P=1-\frac{C^4_5*2^4}{C^4_{10}}=\frac{13}{21}\).
\(C^4_5\) - # of ways to choose 4 different colors out of 5, basically # of ways to choose which 4 color socks will give us one sock (in this case we obviously will have 4 different colors);
\(2^4\) - each of 4 chosen colors can give left or right sock;
\(C^4_{10}\) - total # of ways to choose 4 socks out of 10.
What solution was given in the book for 41/42?