Question

A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers $1,2,3,...,12$ as shown in the figure. What is the probability that it will point to
(i) $6$ ?

(ii) an even number?

(iii) a prime number ?

(iv) a number which is a multiple of $5$?

Answer 1

Total number of outcomes $=12$

(i) Favourable outcome: $6$

No. of favourable outcomes $=1$

$\therefore P$ (Getting $6$) $=\frac{1}{12}$

(ii) Favourable outcomes: $2,4,6,8,10,12$

No. of favourable outcomes $=6$

$\therefore P$ (Getting even number) $=\frac{6}{12}=\frac{1}{2}$

(iii) Favourable outcome: $2,3,5,7,11$

No. of favourable outcomes $=11$

$\therefore P$ (Getting a prime number) $=\frac{5}{12}$

(iv) Favourable outcome: $5,10$

No. of favourable outcomes $=2$

$\therefore P$ (Getting a multiple of $5$) $=\frac{2}{12}=\frac{1}{6}$