When a card is drawn from a well - shuffled deck of 52 cards, the number of possible outcomes is 52.
(i) Let E1
be the event of getting a face card.
Since there are 16 face cards, we have n(E1)=16
.
∴P(E1)=
n(E1)
n(S)
=
16
52
=
4
13
.
⇒
odds in favour of getting a face card
=
P(E1)
{1-P(E1)}
=
(4/13)
(1-
4
13
)
=
4
9
.
(ii) Let E2
be the event of getting a spade. Then, n(E2)=13
.
∴P(E2)=
n(E2)
n(S)
=
13
52
=
1
4
⇒
odds against getting a spade =
{1-P(E2)}
P(E2)
=
(1-
1
4
)
(1/4)
=
3
1
.
