# A Dice is Rolled Twice. Find the Probability that 5 Will Not Come up Either Time - Mathematics

Sum

A dice is rolled twice. Find the probability that  5 will not come up either time

#### Solution

When a dice is rolled twice, all possible outcomes 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)

∴ Total number of outcomes = 36
The outcomes where 5 will not come up either time are
(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 6) So,

the number of favourable outcomes are 25.
∴ P(5 will not come up either time) =$\frac{\text{ Favourable number of outcomes }}{\text{ Total number of outcomes }} = \frac{25}{36}$

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 16 Probability
Exercise 16.1 | Q 64.1 | Page 26