Probability of drawing a 10 not of hearts and another hearts card
Problem 4
Solution
Total number of cards in the pack
= 52
Number of cards drawn
= 2
Experiment :
Drawing 2 cards from the pack of cards
Total Number of Possible Choices
= Number of ways in which 2 cards can be drawn from the 52 cards
⇒ n | = | 52C7 When simplification leads to large calculations leaving the term as it is may help. Simplify when needed in the steps while deriving the required answer. | ||
= |
| |||
= | 26 × 51 | |||
= | 1,326 |
Let
A : the event of drawing a 10 not of hearts and another hearts card
For Event A
10 Not of Hearts | Hearts | Others | Total | |
---|---|---|---|---|
Available | 3 | 12 | 37 | 52 |
To Choose | 1 | 1 | 0 | 2 |
Choices | 3C1 | 12C1 | 37C0 | 52C2 |
Number of Favorable Choices
= Number of ways in which a 10 not of hearts and another hearts card can be drawn from the total 52
= Number of ways in which a 10 not of hearts can be drawn from the available 3 × Number of ways in which a hearts card can be drawn from the available 12
⇒ mA | = | 3C1 × 12C1 | ||||
= |
| |||||
= | 3 × 12 | |||||
= | 36 |
Probability of choosing a 10 not of hearts and another hearts card
⇒ 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 |
= | 1,326 − 36 | |
= | 1,290 |
in favor
Odds in Favor of choosing a 10 not of hearts and another hearts card⇒ Odds in Favor of Event A
= Number of Favorable Choices : Number of Unfavorable Choices
= mA : mAc
= 36 : 1,290
= 6 : 215
against
Odds against choosing a 10 not of hearts and another hearts card⇒ Odds against Event A
= Number of Unfavorable Choices : Number of Favorable Choices
= mAc : mA
= 1,290 : 36
= 215 : 6
Odds (alternative)
Probability of non-occurrence of Event A
⇒ P(Ac) | = | 1 − P(A) | ||
= | 1 −
| |||
= |
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= |
|
in favor
Odds in Favor of choosing a 10 not of hearts and another hearts card⇒ Odds in Favor of Event A
= | Probability of occurrence of the event : Probability of non-occurrence of the event | ||||
= |
| ||||
= | 6 : 215 |
against
Odds against choosing a 10 not of hearts and another hearts card⇒ Odds against Event A
= | Probability of non-occurrence of the event : Probability of occurrence of the event | ||||
= |
| ||||
= | 221 : 6 |