Question

A die is thrown at random. Find the probability of getting
(i) 2
(ii) a number less than 3
(iii) a composite number
(iv) a number not less than 4.

Answer 1

The possible outcomes when a dice is thrown at random are 1, 2, 3, 4, 5 and 6.
Total number of outcomes = 6

(i) ∴​ ${\mathrm{P}}_{\left(\mathrm{getting}2\right)}=\frac{1}{6}$

(ii) The numbers less than 3 are 1 and 2.
Number of possible outcomes = 2
∴​ ${\mathrm{P}}_{\left(\mathrm{getting}\mathrm{a}\mathrm{number}<3\right)}=\frac{2}{6}=\frac{1}{3}$

(iii) A composite number is defined as a number with at least one positive divisor other than itself and unity.
In a dice, 4 and 6 are composite numbers.
Number of possible outcomes = 2
∴​ ${\mathrm{P}}_{\left(\mathrm{getting}\mathrm{a}\mathrm{composite}\mathrm{number}\right)}=\frac{2}{6}=\frac{1}{3}$

(iv) A number not less than 4 can includes 4, 5 or 6.
Number of outcomes = 3
∴${\mathrm{P}}_{\left(\mathrm{getting}\mathrm{a}\mathrm{number}\mathrm{not}\mathrm{less}\mathrm{than}4\right)}=\frac{3}{6}=\frac{1}{2}$