**Probability ncert solutions Chapter 15 Exercise 15.1 Question 12**

**12.** A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and these are equally likely outcomes. What is the probability that it will point at

(i) 8?

(ii) an odd number?

(iii) a number greater than 2?

(iv) a number less than 9?

**Solution (i)**

Let E be the event that arrow rests at number 8.

Number of outcomes favorable to Event E=1

Number of total possible outcomes=8

P(E)=(Number of outcomes favorable to Event E)/(Number of total possible outcomes)=1/8

**Solution(ii)**

Let F be the event that arrow rests at an odd number.

Number of outcomes favorable to Event F=4 (There are 4 odd numbers from numbers 1 to 8)

Total number of possible outcomes=8 (There are total of 8 numbers in the game).

P(F)=(Number of outcomes favorable to Event F)/(Total number of possible outcomes)=4/8=1/2

**Solution (iii)**

Let A be the event that arrow stops at number greater than 2.

Number of outcomes favorable to Event A=6 (There are 6 numbers greater than 2 in a game)

Total number of possible outcomes=8

P(A)=(Number of outcomes favorable to Event A)/(Total number of possible outcomes)=6/8=3/4

**Solution(iv)**

Let B be the event that arrow stops at number less than 9.

Each number in the game is less than 9. Therefore, Event B will certainly happen.

Therefore, P(B)=1