Question

Two dice are thrown at the same time. Find the probability of getting (a) same no. on the both side (b) different

no. on both dices​

Answer 1

Two dice are thrown at the same time.

The possible outcomes are:

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

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

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

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

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

Now,

Probability = (Number of favourable outcomes)/(Total number of outcomes)

a) Same number on the both dices.

Here,

Total number of outcomes = 36

Number of favourable outcomes = 6 [(1,1) (2,2) (3,3) (4,4) (5,5) (6,6)]

So,

P(same number on both dices) = 6/36 = 1/6

b) Different number on both sides.

Here,

Total number of outcomes = 36

Number of favourable outcomes = 36 - 6 = 30 (As 6 are same)

P(different numbers on both dices) = 30/36 = 5/6

Answer 2

$</p><p>\huge{\tt{\pink{Hello!!! }}}$

$Sample Space\: = > \: \begin{cases} 1,1 \: 1,2 \: 1,3 \: 1,4 \: 1,5 \: 1,6 \\2,1 \: 2,2 \: 2,3 \: 2,4 \: 2,5 \: 2,6 \\ 3,1 \: 3,2 \: 3,3 \: 3,4 \: 3,5 \: 3,6 \\ 4,1 \: 4,2 \: 4,3 \: 4,4 \: 4,5 \: 4,6\\ 5,1 \: 5, 2\: 5,3 \: 5,4 \: 5,5 \: 5,6\\ 6,1 \: 6,2 \: 6,3 \: 6,4 \: 6,5 \: 6,6\end{cases}$

$c1 \: => \begin{cases} 11 \\ 22 \\ 33 \\ 44 \\ 55 \\ 66\end{cases}$

$</p><p>\tt{\red{\underline{\boxed {Probability \: 1 \: Of \: Getting \: Same \: No \:On \: Both \: Side \: = \frac{1}{6} }}}}$

$</p><p>\tt{\purple {Probability \: 2 \:= 1 - Probability 1 = \frac{5}{6} }}$