Question

six cards are dealt from a well-shuffled deck. given that all six cards are black, find the probability that they are of same suit.

Answer 1

first card could be of any black suit, so p=1/2
second card must be of the same suit so p=12/52
third card must of the same suit so p=11/52
and so on, the multiply 'em all, i think

Answer 2

\[P(all\ the \ same\ suit)=\frac{1\times 12 \times 11\times 10\times 9\times 8}{2\times 51\times 50 \times 49\times 48\times 47}\]

Answer 3

@Umangiasd After you take the first card, there are 51 left, etc.

Answer 4

If all six cards were drawn with no knowledge of any results, then I'd say the probablity above, @kropot72, is correct, but in this case, we are starting with the knowledge that all six cards are black. Once we know every cards is black, each card can only be of one of two black suits.

Answer 5

@mathstudent55 Your point is correct. So here goes my next attempt:
Given that all six cards are black, the probability that the first card dealt is either a spade or a club is 1. The probability that the second card drawn will be from the same suit as the first is 12/25, the reasons being that only 12 cards remain of the suit dealt first and there are 25 black cards left after the first black card was dealt.
So the required probability is given by
\[P(all\ 6\ cards\ are\ the\ same\ suit)=\frac{12\times 11\times 10\times 9\times 8}{25\times 24\times 23\times 22\times 21} \]