Let S be the sample space. Then,
n(S) = number of ways of drawing 2 cards out of 52
=52C2.
Let E1=
event that both are red cards,
and E2=
event that both are kings.
Then, (E1∩E2)=
event of getting 2 red kings.
∴n(E1)=
number of ways of drawing 2 red cards out of 26 red cards =26C2
.
n(E2)=
number of ways of drawing 2 kings out of 4 kings
=4C2.
∴n(E1∩E2)=
number of ways of drawing 2 red kings out of 2 red kings =2C2=1.
∴P(E1)=
n(E1)
n(S)
=
26C2
52C2
,P(E2)=
n(E2)
n(S)
=
4C2
52C2
.
and P(E1∩E2)=
n(E1∩E2)
n(S)
=
1
52C2
.
∴
P(drawing both red cards or both kings)
=P(E1orE2)=P(E1∪E2)
=P(E1)+P(E2)-P(E1∩E2)
=(
26C2
52C2
+
4C2
52C2
-
1
52C2
)=
(26C2+4C2-1)
52C2
=
(325+6-1)
1326
=
330
1326
=
55
221
.
Hence, the required probability is
55
221
.
