Question

A box contains 100 cards marked with numbers 1 to 100.
If one card is drawn at random from the box, find the
probability that the number on card is (1) a multiple of 7
(2) a number smaller than 30 (3) a prime number.​

Answer 1

Answer:

Refer to the attachment

Answer 2

(1) The probability of a number being a multiple of 7 is 0.14.

(2) The probability of a number being smaller than 30 is 0.29.

(3) The probability of a number being a prime number is 0.25.

Given,

A box contains 100 cards marked with numbers 1 to 100.

To Find,

the  number on the card drawn is (1) a multiple of 7

(2) a number smaller than 30 (3) a prime number.​

Solution,

The formula of probability,

P(E) = n(E) / n(S).

n(E) = Number of favorable outcomes of E.

n(S) = Total number of possible outcomes of E.

(1.) There are 14 numbers multiples of 7 between 1 and 100.

n(E) = 14.

n(S) = 100

P(E) = $\frac{14}{100}$ or 0.14.

(2.) There are 29 numbers that are less than 30.

n(E) = 29

n(S) = 100

P(E) = $\frac{29}{100}$ or 0.29.

(3.) There are 25 prime numbers between 1 and 100.

n(E) = 25

n(S) = 100

P(E) = $\frac{25}{100}$ or 0.25.

(1) The probability of a number being a multiple of 7 is 0.14.

(2) The probability of a number being smaller than 30 is 0.29.

(3) The probability of a number being a prime number is 0.25.

#SPJ2