2016 Question Paper Solution | Question 4

Class 10 Maths Questions

This is an easy 1-mark question from the chapter Probability. Concept tested: Computing the probability of selecting one card from a deck of 52 cards that satisfy the stated condition. The question appeared as a 1-mark question in the CBSE Class 10 board paper in the year 2016.

Question 4: A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.

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Video Explanation

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Explanatory Answer | Q4 2016 Board Paper

Denominator: Number of ways of selecting a card from the pack

A pack of cards has 52 cards.
The number of ways of selecting one card is 52.

Which cards should not be selected? How many such cards form a pack of cards?

The selected card should be neither a red card nor a queen.
Number of red cards in a pack = 26
Number of black queens (queen of spades and queen of clubs)= 2
(Note: We only have to remove black queens as red queens have been removed along with the 26 red cards).
Therefore, the number of cards that should not be selected = 26 + 2 = 28

Numerator: Number of cards in the set from which a card can be selected

The remaining 52 – 28 = 24 cards are neither red cards nor queens.
The number of ways of selecting one of these cards = 24

Probability = \\frac{\text{Number of ways of selecting neither a red card nor a queen}}{\text{Number of ways of selecting 1 card from the pack}}) = \\frac{\text{24}}{\text{52}}) = \\frac{\text{6}}{\text{13}})