A box contains 24 cards numbered 1,2,3,4, ldots, 24 which are mixed thoroughly. A card is drawn at random from the box. Find the probability that the number on the card is prime.

Question

A box contains 24 cards numbered 1,2,3,4, ldots, 24 which are mixed thoroughly. A card is drawn at random from the box. Find the probability that the number on the card is prime. (A) (1/4) (B) (5/8) (C) (3/8) (D) None

Tardigrade Admin · Accepted Answer

Let E be an event that the number on the card is prime. Then E= 2,3,5,7,11,13,17,19,23 n(E)=9 Total possible outcomes n(S)=24 Required probability =(n(E)/n(S))=(9/24)=(3/8)

Q. A box contains 24 cards numbered $1, 2, 3, 4, \dots, 24$ which are mixed thoroughly. A card is drawn at random from the box.
Find the probability that the number on the card is prime.

$\frac{1}{4}$

$\frac{5}{8}$

$\frac{3}{8}$

None

Let $E$ be an event that the number on the card is prime.
Then $E = {2, 3, 5, 7, 11, 13, 17, 19, 23}$
$n (E) = 9$
Total possible outcomes $n (S) = 24$
Required probability $= \frac{n ( E )}{n ( S )} = \frac{9}{24} = \frac{3}{8}$

Q. A box contains 24 cards numbered 1,2,3,4,…,24 which are mixed thoroughly. A card is drawn at random from the box. Find the probability that the number on the card is prime.

41​

85​

83​