Question

Three cards are drawn from a pac of 52 cards find the probability that all the three cards are of the same suit

Answer 1

Answer:

22/425

Step-by-step explanation:

first card may be any card

probability  for second card to be same suit =12/51

probability  for  third card to be same suit    =11/50

so all cards are in same suit is =12x11/(51x50)

                                                   =4x11/(17x50)

                                                    =2x11/(17x25)

                                  =22/425    

Another method

TOTAL cards =52 card

number of cards taken =3

probablity for 3 cards to be HEARTS =13C3/52C3

probablity for 3 cards to be DIAMONDS =13C3/52C3

probablity for 3 cards to be CLAVER =13C3/52C3

probablity for 3 cards to be SPADE  =13C3/52C3

probablity for 3 cards to be SAME SUIT  = 4 X    13C3/52C3

                                                           ={4X13X12X11/1X2X3 }/{52X51X50/1X2X3}

                                                           =12X11/51X50

                                                           =22/425