Question

All the three face cards of spades are removed from a well-shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting

(i) black face card (ii) a queen (iii) a black card

Answer 1

After removing three face cards of spades (king, queen, jack) from a deck of 52 playing cards, there are 49 cards left in the pack. Out of these 49 cards one card can be chosen in 49 ways.

So, Total number of elementary events = 49

(i) There are 6 black face cards out of which 3 face cards of spades are already removed. So, out of remaining 3 black face cards one black face card ban be chosen in 3 ways.

So, Favorable number of elementary events = 3

Hence, P (Getting a black face card ) =3/49

(ii) There are 3 queens in the remaining 49 cards. So, out of these three queens, on queen can be chosen in 3 ways

So, Favorable number of elementary events = 3

Hence P (Getting a queen) =3/49

(iii) There are 23 black cards in the remaining 49 cards, So, out to these 23 black card, one black card can be chosen in 23 ways

So, Favorable number of elementary events = 23

Hence, P (Getting a black card) =23/49