Probability and odds for Drawing/Picking/Choosing an Ace, a Clubs from a Pack of cards
Problem 2
1 |
13 |
1 |
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 an ace.
B : the event of the card drawn being a club.
For Event A
Favorable (Aces) | Unfavorable (Others) | Total | |
---|---|---|---|
Available | 4 | 48 | 52 |
To Choose | 1 | 0 | 1 |
Choices | 4C1 | 48C0 | 52C1 |
Number of Favorable Choices
= Number of ways in which one card can be drawn from the total 4 favorable cards
⇒ mA | = | 4C1 | ||
= |
| |||
= | 4 |
Probability of the card drawn being an ace
⇒ Probability of occurrence of Event A
= |
|
⇒ P(A) | = |
| ||
= |
| |||
= |
|
Odds
Number of Unfavorable Choices= Total Number of possible choices − Number of Favorable choices
⇒ mAc | = | n − mA |
= | 52 − 4 | |
= | 48 |
in favor
Odds in Favor of the card drawn being an ace⇒ Odds in Favor of Event A
= Number of Favorable Choices : Number of Unfavorable Choices
= mA : mAc
= 4 : 48
= 1 : 12
against
Odds against the card drawn being an ace⇒ Odds against Event A
= Number of Unfavorable Choices : Number of Favorable Choices
= mAc : mA
= 48 : 4
= 12 : 1
For Event B
Favorable (Clubs) | Others | Total | |
---|---|---|---|
Available | 13 | 39 | 52 |
To Choose | 1 | 0 | 1 |
Choices | 13C1 | 39C0 | 52C1 |
Number of Favorable Choices
= Number of ways in which one card can be drawn from the total 13 favorable cards
⇒ mA | = | 13C1 | ||
= |
| |||
= | 13 |
Probability of the card drawn being a club
⇒ Probability of occurrence of Event B
= |
|
⇒ P(B) | = |
| ||
= |
| |||
= |
|
Odds
Number of Unfavorable Choices= Total Number of possible choices − Number of Favorable choices
⇒ mAc | = | n − mA |
= | 52 − 13 | |
= | 39 |
in favor
Odds in Favor of the card drawn being a club⇒ Odds in Favor of Event B
= Number of Favorable Choices : Number of Unfavorable Choices
= mB : mBc
= 13 : 39
= 1 : 3
against
Odds against the card drawn being a club⇒ Odds against Event B
= Number of Unfavorable Choices : Number of Favorable Choices
= mBc : mB
= 39 : 13
= 3 : 1