# 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.

**☛ 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

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