Question

Two Cards are drawn from a pack of cards at random. What is the probability that it will be a) A diamomd and a Heart b) A king and a queen C) Two Kings ?

Answer 1

since total cards are 52 in which 13 diamond ,13 hearts , 13 spade ,13 club
in which 4 are kings
4 ace
4 queen
4 jack

now a) to choose a diamond from 13
--> 13 c1=13
and to choose a heart
= 13 c1=13
and to choose two cards from 52 = 52 c2=1326

so prob (a diamond and a heart )
=(13c1*13c1)/52c2
=13*13/1326
=169/1326

b) to choose a king
= 4c1 =4
to choose a queen
= 4c1 =4

so prob ( a queen and a king )
= (4c1*4c1)/52c2
=4*4/1326
=16/1326

c) to choose two kings out of four
= 4c2=6
so prob ( two kings)
= 4c2/52c2
=6/1326