Question

Enter 1 if it is true else enter 0.

A card is drawn at random from a pack of $$52$$ cards. The probability that the card drawn is neither a heart nor a king is $$\dfrac{9}{13}$$.

Answer 1

Correct option is A. 1

To find the probability of drawing a particular card in each case :

Total number of cards in the pack $$= 52$$

Number of spades (black) $$= 13$$

Number of clubs (black) $$= 13$$

Number of hearts (red) $$= 13$$

Number of diamonds (red) $$= 13$$

Probability of an event (P) $$=$$ $$\dfrac{Number\, of\, favorable\, outcomes}{Total\, number\, of\, possible\, outcomes}$$

Probability of drawing a heart or a king $$(P_1)=\dfrac{(Number\, of\, hearts + Number\, of\, kings\, in\, spades, clubs, and\, diamonds)}{Total\, number\, of \,cards}$$

$$\Rightarrow$$ $$P_1 =\dfrac{13+3}{52}=\dfrac{16}{52}=\dfrac{4}{13}$$

Now,

$$\Rightarrow$$ Probability of drawing neither a heart nor a king $$(P) = 1 -$$ Probability of drawing a heart or a king

$$\Rightarrow$$ $$P = 1 - \dfrac{4}{13}$$

$$\Rightarrow$$ $$P = \dfrac{13-4}{13}$$

$$\Rightarrow$$ $$P=\dfrac{9}{13}$$