A card is selected from a pack of 52 cards. I. The probability that card is an ace of spades, is (2/52). II. The probability that the card is black card, is (1/2).

Question

A card is selected from a pack of 52 cards. I. The probability that card is an ace of spades, is (2/52). II. The probability that the card is black card, is (1/2). (A) Only I is false. (B) Only II is false. (C) Both I and II are false. (D) Both I and II are true.

Tardigrade Admin · Accepted Answer

There is 1 ace of spade. ∴ n(A)=1, n(S)=52 Probability that the card drawn is an ace of spade =(n(A)/n(S))=(1/52) II. There are 26 black cards. n(A)=26, n(S)=52 Probability of getting a black card =(26/52)=(1/2)

Q. A card is selected from a pack of $52$ cards.
I. The probability that card is an ace of spades, is $\frac{2}{52}$ .
II. The probability that the card is black card, is $\frac{1}{2}$ .

Only I is false.

Only II is false.

Both I and II are false.

Both I and II are true.

There is $1$ ace of spade.
$∴ n (A) = 1, n (S) = 52$
Probability that the card drawn is an ace of spade
$= \frac{n ( A )}{n ( S )} = \frac{1}{52}$
II. There are $26$ black cards.
$n (A) = 26, n (S) = 52$
Probability of getting a black card $= \frac{26}{52} = \frac{1}{2}$

Q. A card is selected from a pack of 52 cards. I. The probability that card is an ace of spades, is 522​. II. The probability that the card is black card, is 21​.