Question

Choose the correct alternative answer for each of the following questions.
(1)Which number cannot represent a probability ?

(A) $\frac{2}{3}$

(B) 1.5

(C) 15%

(D) 0.7

(2) A die is rolled. What is the probability that the number appearing on upper face is less than 3 ?

(A) $\frac{1}{6}$

(B) $\frac{1}{3}$

(C) $\frac{1}{2}$

(D) 0

(3) What is the probability of the event that a number chosen from 1 to 100 is a prime number ?

(A) $\frac{1}{5}$

(B) $\frac{6}{25}$

(C) $\frac{1}{4}$

(D) $\frac{13}{50}$

(4) There are 40 cards in a bag. Each bears a number from 1 to 40. One card is drawn at random. What is the probability that the card bears a number which is a multiple of 5 ?

(A) $\frac{1}{5}$

(B) $\frac{3}{5}$

(C) $\frac{4}{5}$

(D) $\frac{1}{3}$

(5) If n(A) = 2, P(A) = $\frac{1}{5}$ , then n(S) = ?

(A) 10

(B) $\frac{5}{2}$

(C) $\frac{2}{5}$

(D) $\frac{1}{3}$

Answer 1

(1)
The probability cannot be greater than 1.
Hence, the correct option is (B).
(2)
Sample Space (S) = {1, 2, 3, 4, 5, 6}
∴ n(S) = 6
Event A: a number is less than 3
A = {1, 2}
∴ n(A) = 2
$$\begin{gathered} \therefore \mathrm{P}\left(\mathrm{A}\right)=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{n}\left(\mathrm{S}\right)} \\ =\frac{2}{6} \\ =\frac{1}{3} \end{gathered}$$
​Hence, the correct option is (B).

(3)
Sample Space (S) = {1, 2, ......, 100}
∴ n(S) = 100
Event A: a prime number
A = {2, 3, 5,.....97}
∴ n(A) = 25
$$\begin{gathered} \therefore \mathrm{P}\left(\mathrm{A}\right)=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{n}\left(\mathrm{S}\right)} \\ =\frac{25}{100} \\ =\frac{1}{4} \end{gathered}$$
​Hence, the correct option is (C).

(4)
Sample Space (S) = {1, 2, ......, 40}
∴ n(S) = 40
Event A: a multiple of 5
A = {5, 10, 15, 20, 25, 30, 35, 40}
∴ n(A) = 8
​$$\begin{gathered} \therefore \mathrm{P}\left(\mathrm{A}\right)=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{n}\left(\mathrm{S}\right)} \\ =\frac{8}{40} \\ =\frac{1}{5} \end{gathered}$$
​Hence, the correct option is (A).

(5)
$$\begin{gathered} \mathrm{P}\left(\mathrm{A}\right)=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{n}\left(\mathrm{S}\right)} \\ \Rightarrow \mathrm{n}\left(\mathrm{S}\right)=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{P}\left(\mathrm{A}\right)} \\ =\frac{2}{{\displaystyle \frac{1}{5}}} \end{gathered}$$
= 10
​Hence, the correct option is (A).