Question

After removing two black face cards from a pack of 52 playing cards if one card is drawn from the remaining cards, the probability of getting a card of clubs is .​

Answer 1

Answer:

Step-by-step explanation:

2 black Kings, 2 black queen and 2 black jack are removed from the Deck of 52 playing cards.

So, remaining cards in deck = 52 - 6 = 46

Total number of outcomes = 46

(i) We know ,that there are 12 face cards.

6 black face cards are removed.

Remaining face cards = 12 - 6 = 6  

Let E1 = Event of getting a face card

Number of favourable outcomes to E1= 6

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

P(E1) = 6/46 = 3/23

Hence, the Required probability of getting a face card , P(E1) = 13/46

 

ii) We know ,that there are 26 red cards in a deck.  

Let E2 = event of getting a red card  

Number of favourable outcomes to  E2 = 26

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

P(E2) = 26/46 = 13/23

Hence, the Required probability of getting a red card,  P(E2) = 13/23

 

(iii) We know, that there are 26 black cards in a Deck .6 black face cards are removed Remaining black cards are = 26 - 6 = 20

Let E3 = Event of getting a black card

Number of favourable outcomes to  E3 = 20

Required probability P(E3) = Number of favourable outcomes / total number of outcomes

P(E3) = 20/46 = 10/23

Hence, the Required probability of getting a black card,  P(E3) = 10/23 .

 

(iv) We know ,that there are (2 black + 2 red) 4 king cards in a deck. 2 black kings are removed.

Remaining king card left = 4 - 2 = 2

Let E4 = Event  of getting a king  card

Number of outcome favourable to E4 = 2

Probability (E4) = Number of favourable outcomes / Total number of outcomes

P(E4) = 2/46 = 1/23

Hence, the required probability of getting a king  card , P(E4) = 1/23.