Odds against a gambler winning a bet that a card drawn from a pack of ordinary cards is a spade or an ace
Problem 5
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 this bet?
Ans : 9 : 4
Solution
Experiment :
Drawing a card from a pack of 52 cards
Total Number of Possible Choices
= Number of ways in which one card can be drawn from the total 52
⇒ n | = | 52C1 | ||
= |
| |||
= | 52 |
Let
A : the event of the card drawn being a spade or an ace.
For Event A
Favorable (Spades + Aces) | Unfavorable (Others) | Total | |
---|---|---|---|
Available | 16 | 36 | 52 |
To Choose | 1 | 0 | 1 |
Choices | 16C1 | 36C0 | 52C1 |
Number of Favorable Choices
= Number of ways in which one card can be drawn from the total 16 favorable cards
⇒ mA | = | 16C1 | ||
= |
| |||
= | 16 |
Odds
Number of Unfavorable Choices= Total Number of possible choices − Number of Favorable choices
⇒ mAc | = | n − mA |
= | 52 − 16 | |
= | 36 |
Odds against the gambler winning the bet
⇒ Odds against the card drawn being a spade or an ace.
⇒ Odds against Event A
= Number of Unfavorable Choices : Number of Favorable Choices
= mAc : mA
= 36 : 16
= 9 : 4
Author : The Edifier