Question

All jacks, queens and kings 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 black face card
(ii)a red card.

Answer 1

SOLUTION:

Given :  All kings ,queens & jacks cards are removed from a pack of 52 cards .

King, queen ,and jack are called face cards. Total number of face cards are 12.

So, remaining cards in deck = 52 - 12 = 40

Total number of outcomes = 40

(i)Let E1 = Event of getting a black face card

All the black face cards are removed

Number of favourable outcomes to E1 = 0

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

P(E1) = 0/40 = 0

Hence, the probability of getting a black face card , P(E1) = 0

ii) We know ,that there are 26 red cards in a deck. 6 red face cards  are removed from the deck .

Remaining red cards in a deck = 26 - 6 = 20

Let E2 = Event of getting a red card  

Number of favourable outcomes to  E2 = 20

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

P(E2) = 20/40 = 1/2

Hence, the probability of getting a red 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,jack and queens are removed from a pack of 52 cards.
So, Cards left in the deck are 52-12= 40

Total outcomes = 40

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

Favourable outcome = 0

Since,no face card is left in the deck.

Probability of drawing a red face card = 0/40

= 0

2) A Red card:

Favourable outcome: 10+10= 20

(10 cards of HEART and 10 cards of DIAMOND)

Probability of drawing a black card = 20/40

= 1/2

Hope it helps you.