A card is drawn at random from a well-shuffled pack of 52 cards.

Question:

A card is drawn at random from a well-shuffled pack of 52 cards. What is the probability that the card bears a number greater than 3 and less than 10?

 

Solution:

We know that,

Probability of occurrence of an event

$=\frac{\text { Total no. of Desired outcomes }}{\text { Total no.of outcomes }}$

Total no. of outcomes are 52

Desired output is a number greater than 3 and less than 10 .

There will be four sets of each card naming $A, 1,2,3,4,5,6,7,8,9,10, J, Q, K .$ So, there will be a total of 24 cards between 3 and 10

Therefore, the probability of picking card between 3 and $10=\frac{24}{52}$

$=\frac{6}{13}$

Conclusion: Probability of picking a card between 3 and 10 is $\frac{6}{13}$

 

 

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