Choosing a card with a prime number less than 20 on it

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Problem 2

A card is drawn from a pack of 52 cards numbered 2 to 53. the probability and odds that the number on the card is a prime number less than 20 is
Ans :
2
13
, 2 : 11, 11 : 2

Solution

Total number of cards

= 52

Experiment :

Drawing a card from the 52 cards marked 2 to 53

Total Number of Possible Choices

= Number of ways a card with a prime number less than 20 can be drawn from the total 52

⇒ n = 52C1
=
52
1
= 52

Let

A : the event of drawing a card with a prime number less than 20 on it

For Event A

Prime numbers less than 20 and ≥ 2

= 8 {2, 3, 5, 7, 11, 13, 17, 19}

Favorable
(2 ≤ Prime Numbers < 20 ) 		Unfavorable
(Others) 		Total
Available 8 44 52
To Choose 1 0 1
Choices 8C144C052C1

Number of Favorable Choices

= Number of ways in which one card with a prime number less than 20 can be drawn from the total 8 favorable cards

⇒ mA = 8C1
=
8
1
= 8

Probability of drawing a card with a prime number less than 20 from the available cards

⇒ 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
=
8
52
=
2
13

Odds

Number of Unfavorable Choices

= Total Number of possible choices − Number of Favorable choices

⇒ mAc = n − mA
= 52 − 8
= 44

in favor

Odds in Favor of drawing a card with a prime number less than 20

⇒ Odds in Favor of Event A

= Number of Favorable Choices : Number of Unfavorable Choices

= mA : mAc

= 8 : 44

= 2 : 11

against

Odds against drawing a card with a prime number less than 20

⇒ Odds against Event A

= Number of Unfavorable Choices : Number of Favorable Choices

= mAc : mA

= 44 : 8

= 11 : 2

Author : The Edifier
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