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Determine the probability that the card is a heart if the king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards

Solution:

Given, the king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled.

We have to determine the probability of drawing a heart.

A deck of 52 playing cards has 13 cards of heart, 13 cards of diamond, 13 cards of spade and 13 cards of club.

King, queen and jack of clubs are removed.

So, remaining cards = 52 - 3 = 49

The probability of drawing a heart is given by

Favourable outcomes = 13 cards of heart

Number of favourable outcomes = 13

Number of possible outcomes = 49

Probability = number of favourable outcomes / number of possible outcomes

Probability = 13/49

Therefore, the probability of drawing a heart is 13/49.

✦ Try This: The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is a spade.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 14

NCERT Exemplar Class 10 Maths Exercise 13.3 Problem 28(i)

Determine the probability that the card is a heart if the king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards

Summary:

The king, queen and jack of clubs are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. The probability that the card is a heart is 13/49

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