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 ?


Total numbers of elementary events are: 12

(i) Let E be the event of getting arrow pointed to 6


Then, the favourable outcome is: 1


∴ P (getting 6) =P (E) = 1/12


(ii) Let E be the event of getting an even number


The favourable numbers are: 2, 4, 6, 8, 10, 12


Then, the number of favourable outcomes are = 6


∴ P (an even number) = P (E) = 6/12 = 1/2


(iii) Let E be the elementary event of getting a prime number


The favourable numbers are: 2, 3, 5, 7, 11


Then, the number of favourable outcomes = 5


∴ P (prime number) = P (E) = 5/12


(iv) Let E be the event of getting a number which is perfect square


The favourable numbers are: 4, 9


Then, the favourable outcomes = 2


∴ P (perfect square number) = P (E) = 2/12 = 1/6


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