A and B alternatively cut Pack of Cards and Pack is shuffled after each cut.If a starts the game and is continued till one gets a club.Then the chance that B cuts the club first in 3rd trial is?
-
Do the cards get replaced between cuts?
If B gets club first in 3rd trial, then we get:
1st trial: A doesn't get club, B doesn't get club
2nd trial: A doesn't get club, B doesn't get club
3rd trial: A doesn't get club, B gets club
With replacement:
Prob = (3/4)^5 * (1/4) = 243/4096 = 5.93 %
Without replacement:
Deck starts with 39 non-clubs and 13 clubs
Prob = (39/52) (38/51) (37/50) (36/49) (35/48) (13/47) = 0.061275 = 6.13%
If B gets club first in 3rd trial, then we get:
1st trial: A doesn't get club, B doesn't get club
2nd trial: A doesn't get club, B doesn't get club
3rd trial: A doesn't get club, B gets club
With replacement:
Prob = (3/4)^5 * (1/4) = 243/4096 = 5.93 %
Without replacement:
Deck starts with 39 non-clubs and 13 clubs
Prob = (39/52) (38/51) (37/50) (36/49) (35/48) (13/47) = 0.061275 = 6.13%
-
P = P(not a club) x P(not a club) x P(club) = 3/4 x 3/4 x 1/4 = 9 / 64