PLAYING CARDS PROBABILITY WORKSHEET

Problem 1 :

A card is drawn at random from a well shuffled pack of 52 cards. What is the probability that the drawn card is king ?

Problem 2 :

A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that the drawn card is not king.

Problem 3 :

A card is drawn at random from a well shuffled pack of 52 cards. What is the probability that the card is neither a spade nor a Jack ?

Answers

Problem 1 :

A card is drawn at random from a well shuffled pack of 52 cards. What is the probability that the drawn card is king ?

Solution : 

Let A be the event of drawing a king card. 

There are 4 king cards in total. 

Then, 

n(A)  =  4

And also

n(S)  =  52

Required probability is

P(A)  =  n(A)/n(S)

P(A)  =  4/52  =  1/13

So, the probability of getting a kind card is 1/13.

Problem 2 :

A card is drawn at random from a well shuffled pack of 52 cards. Find the probability that the drawn card is not king.

Solution :

Let A be the event of drawing a card that is not king. 

There are 4 king cards in the pack of 52 cards.

Then, the number of cards which are not king :

n(A)  =  52 - 4

n(A)  =  48

And also

n(S)  =  52

Required probability is

P(A)  =  n(A)/n(S)

P(A)  =  48/52

P(A)  =  12/13

So, the probability of getting a kind card is 12/13.

Problem 3 :

A card is drawn at random from a well shuffled pack of 52 cards. What is the probability that the card is neither a spade nor a Jack ?

Solution :

Let A be the event of drawing a card that is neither spade nor Jack. 

There are 13 spade cards in a pack of 52 cards. 

(Jack in spade is already included in these 13 cards)

In the remaining 3 types (club, heart, diamond), there are 3 jack cards. 

Number of spade cards and jack cards is

=  13 + 3

=  16 

So, no.of cards which are neither spade nor Jack  are

=  52 - 16

=  36

Then,

n(A)  =  36

And also

n(S)  =  52

Required probability is

P(A)  =  n(A)/n(S)

P(A)  =  36/52

P(A)  =  9/13

So, the required probability is 9/13.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.