**Probability ncert solutions Chapter 15 Exercise 15.1 Question 24**

**24.** A die is thrown twice. What is the probability that

(i) 5 will not come up either time? (ii) 5 will come up at least once?

[**Hint:** Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]

**Solution:**

The different outcomes possible when throwing two dice are:

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

**(i)**

Let E be the event that 5 does not appear either time.

Number of outcomes favorable to event E=25

Total number of possible outcomes=36

P(E)=(Number of outcomes favorable to Event E)/(Total number of possible outcomes)

**(ii)**

Let F be the even that 5 appear at least once.

Number of outcomes favorable to event E=11

Total number of possible outcomes=36

P(F)=(Number of outcomes favorable to Event F)/(Total number of possible outcomes)