Question

All kings and queens are removed from a pack of 52 cards. The remaining cards are well shuffled and then a card is randomly drawn from it. Find the probability that this card is
(i)a red face card
(ii)a black card.

Answer 1

SOLUTION:

Given :  All kings and queens cards are removed from a pack of 52 cards .

In the pack of 52 playing cards there are 4 queen and 4 king .

So, remaining cards in deck = 52 - (4 + 4) = 52 - 8 = 44

Total number of outcomes = 44

(i) We know ,that there are 12 face cards. 4  kings ,4 queens and 4 jacks.

4  kings & 4 queens are removed. 4 jacks are left i.e 2 red & 2 black  

Red face cards = 2

Let E1 = Event of getting a red face card

Number of favourable outcomes to E1 = 2

Required probability P(E1) = Number of favourable outcomes / total number of outcomes

P(E1) = 2/44 = 1/22

Hence, the probability of getting a red face card , P(E1) = 1/22

ii) We know ,that there are 26 black cards in a deck. There are 2 black kings & 2 black queens in a deck. 4 black cards(kings & queens)  are removed from the deck .

Remaining black cards in a deck = 26 - 4 = 22

Let E2 = Event of getting a black card  

Number of favourable outcomes to  E2 = 22

Probability P(E2) = Number of favourable outcomes / total number of outcomes

P(E2) = 22/44 = 1/2

Hence, the probability of getting a black card,  P(E2) = ½ .

HOPE THIS ANSWER WILL HELP  YOU….

Answer 2

Solution:

A deck of cards have 4 suits,i.e.

13 cards of CLUB

13 cards of SPADE

13 cards of HEART

13 cards of DIAMOND

Each suit have 3 face cards(King, Queen and Jack)

As All kings and queens are removed from a pack of 52 cards.
So, Cards left in the deck are 52-8= 44

Total outcomes = 44

1)Find the probability that the card drawn is
a red face card :

Favourable outcome = 2

{ Jack of Heart, Jack of Diamond}

Probability of drawing a red face card = 2/44

= 1/22

2) A black card:

Favourable outcome: 11+11= 22

(11 cards of club and 11 cards of spade)

Probability of drawing a black card = 22/44

= 1/2

Hope it helps you.