# 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:**

Total number of outcomes when die is thrown twice = 6 × 6 = 36.

(i) Number of possible outcomes when 5 will come up either time = (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (1, 5), (2, 5), (3, 5), (4, 5), (6, 5) = 11

Probability that 5 will come up either time = Number of possible outcomes/Total number of favourable outcomes

= 11/36

The probability that 5 will not come up either time = 1 - 11/36

= 25/36

(ii) Number of possible outcomes when 5 will come up at least once = 11

The probability that 5 comes up at least once = Number of possible outcomes/Total number of favourable outcomes

= 11/36

The probability that 5 will not come up either time is 25/36 and the probability that 5 will come up is 11/36.

Check out more about terms of probability.

**ā Check: **NCERT Solutions for Class 10 Maths Chapter 15

**Video Solution:**

## 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]

NCERT Solutions for Class 10 Maths Chapter 15 Exercise 15.1 Question 24

**Summary:**

A die is thrown twice.The probability that (i) 5 will not come up either time is 25/36 and (ii) 5 will come up at least once is 11/36

**ā Related Questions:**

- A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5.
- A child has a die whose six faces show the letters as given below:The die is thrown once. What is the probability of getting(i) A?(ii) D?
- Suppose you drop a die at random on the rectangular region shown in Fig. 15.6. What is the probability that it will land inside the circle with diameter 1m?
- A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that (i) She will buy it ? (ii) She will not buy it ?

visual curriculum