Question

all the 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(a) a black card(b) a queen

Answer 1

Total no. of cards in a deck = 52
When all the face cards of spade are removed from the deck , total cards in deck = 49
total possible outcomes = 49

(a) no. of black cards in the deck = 23
no. of favorable outcomes = 23
$\mathrm{required}\mathrm{probability}=\frac{\mathrm{no}.\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{total}\mathrm{possible}\mathrm{outcomes}}=\frac{23}{49}$

(b) no. of queens in a deck = 3
no. of favorable outcomes = 3
$\mathrm{required}\mathrm{probability}=\frac{\mathrm{no}.\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{total}\mathrm{possible}\mathrm{outcomes}}=\frac{3}{49}$