Question

Two dice are thrown at the same time. Find the probability of getting different number on both dice

Answer 1

make this table for easier solve
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

hence the probability is  30/36 = 5/6

Answer 2

Given:

• Two dice are thrown at the same time.

To Find

Probability of

• Different numbers on both dice.

Solution:

Let the event of getting a different number on both dice be x

$\\ {\green{\boxed{\underline{\tt\large{ n(x) = Total \ outcomes - Outcomes \ for \ the \ same \ number }}}}}$

• Number of possible outcomes = n(x)

• Total Numbers of Outcomes = 36

• Number of possible outcomes for the same number on both dice = 6

Putting values,

$\implies$ 36 – 6

$\implies$ 30

Therefore,

• The required probability = P(B) = n(B) /n(S)

$\implies{\tt{ \dfrac{ \cancel{30} }{ \cancel{36} } }}$

$\implies {\boxed{\tt\large\pink{ \dfrac{5}{6} }}}$

Hence,

• Probability of getting different number on both dice is 5/6 .