Question

Q.10 A card is drawn from an ordinary pack and a gambler bets that it is a spade or an ace. What are the odds against his winning the bet?​

Answer 1

Given A card is drawn from a pack of well-shuffled 52 cards and a gambler bets that it is a spade or an ace. What are the odds against his winning this bet?

A pack of cards has 13 spades. There are 4 aces.

Now we can pick either ace or a spade.

The ace of spades include 13 spades and 3 aces in the remaining cards.

So we can choose 13 + 3 = 16

The total number of choice will be 52

One card could be drawn is 16 C1

So 52 – 16 = 36

Now odds against the gambler winning the bet will be

Number of not favourable choice : number of favourable choice

36: 16

9 : 4

Answer 2

Step-by-step explanation:

Let events A: a spade is drawn and event B: an ace is drawn.

The probability of winning the bet=P(A or B)

P(AorB)=P(A)+P(B)−P(A∩B)

=

52

13

+

52

4

−

52

1

(There is one ace of spades)

=

52

16

=

13

4

∴ Probability of losing the bet=1−

13

4

=

13

9

∴ Odds against winning the bet=

13

9

:

13

4

=9:4.

I hope this help us to u