 # The king, the jack and the 10 of spades are lost from a pack of 52 cards and a card is drawn from the remaining cards after shuffling.

Question:

The king, the jack and the 10 of spades are lost from a pack of 52 cards and a card is drawn from the remaining cards after shuffling. Find the probability of getting a
(i) red card
(ii) black jack
(iii) red king
(iv) 10 of hearts.

Solution:

Total number of cards in a deck is 52.
The number of cards left after loosing the King, the Jack and the 10 of spade = 52-">3 = 49.
(i) Red card left after loosing King, the Jack and the 10 of spade will be 13 hearts + 13 diamond = 26 cards

$P($ red card $)=\frac{26}{49}$

(ii) Black jack left after loosing King, the Jack and the 10 of spade will be one only of club.

$P($ black jack $)=\frac{1}{49} .$

(iii) Red king left after loosing King, the Jack and the 10 of spade will be red of diamond and red of hearts i.e two cards.

$P($ red king $)=\frac{2}{49}$

(iv) 10 of hearts will be one only after loosing King, the Jack and the 10 of spade

$P(10$ of hearts $)=\frac{1}{49} .$