# Question 6 Exercise 6.4

Solutions of Question 6 of Exercise 6.4 of Unit 06: Permutation, Combination and Probablity. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.

## Question 6(i)

If one card is drawn at random from a well shuffled pack of $52$ cards. Then find the probability of each of the Drawing an ace card.

### Solution

Total cards $$=52$$ An ace. Total ace cards $=4$. Hence the probability of getting ace card is: $$=\dfrac{4}{52}=\dfrac{1}{13}$$

## Question 6(ii)

If one card is drawn at random from a well shuffled pack of $52$ cards. Then find the probability of each of the Drawing either spade or hearıs.

### Solution

Total cards $=52$

Drawing either space or hearts

Total number of spade in deck of cards are $13$

total number of hearts are also $13$

Thus the probability of getting spacte or hcart is: $$\dfrac{13}{52}+ \dfrac{13}{52}=\dfrac{1}{4}+\dfrac{1}{4}=\dfrac{2}{4}=\dfrac{1}{2}$$

## Question 6(iii)

If one card is drawn at random from a well shuffled pack of $52$ cards. Then find the probability of each of the Drawing a diamond card.

### Solution

Total cards $=52$

Drawing a diamond card.

Total number of diamond cards in deck of eards is $13.$

Hence the probability of getting diamond card is: $$=\dfrac{13}{52}=\dfrac{1}{4}$$

## Question 6(iv)

If one card is drawn at random from a well shuffled pack of $52$ cards. Then find the probability of each of the Drawing a face card.

### Solution

Total cards $=52$(iv) Drawing a face card.

The total number of face cards in deck of card are $12.$

Thus the probability of getting a face card is: $$=\dfrac{12}{52}=\dfrac{3}{13}$$

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