Two people are playing Snap with exactly half a deck of cards each (total 52).
What is the probability of there being no matches after four cards (in total) have been played?
My thinking is as follows (but it's wrong):
52/52 * 48/51 * ((44/50 * 46/49) + (3/50 * 47/49) + (3/50 * 47/49))
Explanation:
[FONT="]52 ways to draw the first card, 48 non-matches for card 2.
[/FONT]Then the 3rd and 4th cards could be either:
- an unseen card rank is drawn for card 3 (44/50) plus a non-match (46/49) OR
- card 3 is the same as card 1 (3/50) plus a non-match (47/49) OR
- card 3 is the same as card 2 (3/50) plus a non-match (47/49)
This equals approx 0.88, however the correct answer is approx 0.83.
Can anyone help?
What is the probability of there being no matches after four cards (in total) have been played?
My thinking is as follows (but it's wrong):
52/52 * 48/51 * ((44/50 * 46/49) + (3/50 * 47/49) + (3/50 * 47/49))
Explanation:
[FONT="]52 ways to draw the first card, 48 non-matches for card 2.
[/FONT]Then the 3rd and 4th cards could be either:
- an unseen card rank is drawn for card 3 (44/50) plus a non-match (46/49) OR
- card 3 is the same as card 1 (3/50) plus a non-match (47/49) OR
- card 3 is the same as card 2 (3/50) plus a non-match (47/49)
This equals approx 0.88, however the correct answer is approx 0.83.
Can anyone help?