Probability and odds for not Drawing/Picking/Choosing a jack or a king from a Pack of cards

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Problem 4

From a normal pack of cards, a card is drawn at random. Find the probability and odds of not getting a jack or a king.
Ans :
9
13
, 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
1
= 52

Let

A : the event of not getting a jack or a king.

For Event A

Favorable
(Others) 		Unfavorable
(Jacks + Kings) 		Total
Available 44 8 52
To Choose 1 0 1
Choices 44C18C052C1

Number of Favorable Choices

= Number of ways in which one card can be drawn from the total 44 favorable cards

⇒ mA = 44C1
=
44
1
= 44

Probability of not getting a jack or a king.

⇒ Probability of occurrence of Event A

=
Number of Favorable Choices for the Event
Total Number of Possible Choices for the Experiment
⇒ P(A) =
mA
n
=
44
52
=
11
13

Odds

Number of Unfavorable Choices

= Total Number of possible choices − Number of Favorable choices

⇒ mAc = n − mA
= 52 − 44
= 8

in favor

Odds in Favor of not getting a jack or a king.

⇒ Odds in Favor of Event A

= Number of Favorable Choices : Number of Unfavorable Choices

= mA : mAc

= 44 : 8

= 11 : 2

against

Odds against not getting a jack or a king.

⇒ Odds against Event A

= Number of Unfavorable Choices : Number of Favorable Choices

= mAc : mA

= 8 : 44

= 2 : 11

Author : The Edifier
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