Question

Mark the correct alternative in each of the following: Two dice are thrown together. The probability of getting the same number on both dice is
(a)$\frac{1}{2}$
(b)$\frac{1}{3}$
(c)$\frac{1}{6}$
(d)$\frac{1}{12}$

Answer 1

SOLUTION :

The correct option is (c) : 1/6

Given : A pair of dice is thrown  

If we throw two dices then there possible outcomes are as follows:

{(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 no. of possible outcomes when 2 dice are thrown = 6 x 6 = 36

Total Number of possible outcomes = 36

Let E = Event of getting a same number on both the dice

Favorable outcomes (same number on both the dice) :  

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

Number of favorable outcomes = 6

Probability = Number of favourable outcomes / total number of outcomes

P(E) = 6/36 = ⅙  

Hence, the Probability of getting a same number on both the dice, P(E) = 1/6

HOPE THIS ANSWER WILL HELP  YOU….

Answer 2

Number of favourable outcomes = 1,1;2,2:3,3;4,4;5,5;6,6 total equal to 6.

Total number of favourable outcomes=32

So, the probability is 6/32

=>1/6

option D.