A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number, 1,2,3,….,12 as shown in figure. What is the probability that it will point to:(iii) a number which is multiple of 3? (iv) an even number?
A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number, 1,2,3,….,12 as shown in figure. What is the probability that it will point to:(iii) a number which is multiple of 3? (iv) an even number?

(iii) So, Favorable outcomes i.e. to get a multiple of 3 are 3,6,9, and 12

Therefore, total number of favorable outcomes i.e. to get a multiple of 3 is 4

We know that the Probability = Number of favorable outcomes/ Total number of outcomes

Hence, the probability of getting multiple of 3=4/12=1/3

(iv) Now, Favorable outcomes i.e. to get an even number are 2,4,6,8,10, and 12

Therefore, total number of favorable outcomes i.e. to get an even number is 6

We know that the Probability = Number of favorable outcomes/ Total number of outcomes

Hence, the probability of getting an even number =6/12=1/2