Question

All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is
(i)a red card
(ii)a face card and
(iii)a card of clubs.

Answer 1

★★ A deck of playing cards consists of 52 cards out of which 26 are black cards and  other 26 are red cards, where red cards consists of 13 cards of heart(♥️) ,13 cards of diamond(♦️) and black cards consists of 13 cards  of spades(♠️)and 13 cards are club(♣️).

★★13 cards in each suit are ace,king ,queen, Jack, 10, 9,8,7,6, 5, 4, 3 and 2.

★★ King, queen ,and jack are called face cards.

★★ Total number of face cards are 12.

SOLUTION :  

Given : Total number of cards in one Deck = 52

6 red face cards  are removed from the deck .

Number of remaining cards in one deck = 52 - 6  = 46

Total number of outcomes = 46

(i) Let E1 = Event  of getting a red card  

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

Number of outcome favourable to E1 = 20

Probability (E1) = Number of favourable outcomes / Total number of outcomes

P(E1) = 20/46  = 10/23

Hence, the  probability of getting a red card , P(E1) = 10/23 .

(ii) Total number of face cards = (6 red + 6 black ) =  12

6 red face cards are Removed  

Number of face cards left = 12 - 6 = 6

Let E2 = Event  of getting a face card  

Number of outcome favourable to E2 = 6

Probability (E2) = Number of favourable outcomes / Total number of outcomes

P(E2) = 6/46 = 3/23

Hence, the  probability of getting a face card  , P(E2) = 3/23 .

(iii) Total number of club cards = 13

Let E3 = Event  of getting a club card  

Number of outcome favourable to E3 = 13

Probability (E3) = Number of favourable outcomes / Total number of outcomes

P(E3) = 13/46

Hence, the probability of getting a club card , P(E3) = 13/46 .

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

$\mathbb{\red{\huge{HEY\:MATE}}}$

$\boxed{HERE\:IS\:YOUR\:ANSWER}$

$\mathfrak{\green{ANSWER:}}$

i) There are 12 face cards in all in pack of 52 cards.Out of that there are 6 red face cards. (52 - 6 = 46)
Out of 12 face cards, 6 red face cards are removed.hence, remaining red cards = 26 - 6= 20
The probability of getting the red from remaining 46 cards = 20/46 = 10/23

ii) TOTAL FACE CARDS=12
RED FACE CARDS =6
LEFT FACE CARDS =12-6 =6

PROBABILITY = 6/46=3/23

iii)There are 13 clubs  cards in all in pack of 52 cards.
Out of that there are 6 red face cards. (52 - 6 = 46)

hence the probability of getting clubs card from remaining 46 cards = 13/46 .

$<marquee>$❣❣HOPE IT HELPS U ❣❣

$<marquee>$❣❣PLEASE MARK MY ANSWER AS BRAINLILIST ❣❣

$<marquee>$❣❣THANKS ❣❣

☺☺☺

$\boxed{BE BRAINLY}$