# $A$ and $B$ throw a pair of dice respectively. If $A$throws die such that the total of the numbers on the dice is$9$, find chance of throwing a higher number than $A$ .

Last updated date: 15th Mar 2023

•

Total views: 306.6k

•

Views today: 7.86k

Answer

Verified

306.6k+ views

Hint:For this question we are going to consider all outcomes, out of which we are going to select only those pairs whose sum is greater than .

A single throw of dice can have $36$ i.e. $6 \times 6$ outcomes. So, let us take a look at all the $36$ outcomes.

$\left( {1,1} \right)\left( {1,2} \right)\left( {1,3} \right)\left( {1,4} \right)\left( {1,5} \right)\left( {1,6} \right)$

$\left( {2,1} \right)\left( {2,2} \right)\left( {2,3} \right)\left( {2,4} \right)\left( {2,5} \right)\left( {2,6} \right)$

$\left( {3,1} \right)\left( {3,2} \right)\left( {3,3} \right)\left( {3,4} \right)\left( {3,5} \right)\left( {3,6} \right)$

$\left( {4,1} \right)\left( {4,2} \right)\left( {4,3} \right)\left( {4,4} \right)\left( {4,5} \right)\left( {4,6} \right)$

$\left( {5,1} \right)\left( {5,2} \right)\left( {5,3} \right)\left( {5,4} \right)\left( {5,5} \right)\left( {5,6} \right)$

$\left( {6,1} \right)\left( {6,2} \right)\left( {6,3} \right)\left( {6,4} \right)\left( {6,5} \right)\left( {6,6} \right)$

Now, it is given that the total on the dice of $A$ is $9$.

Let E be the event of getting a number on $B$’s dice that is greater than $9$

Number of favourable outcomes= $6$(i.e.$(4,6),(5,5),(5,6),(6,4),(6,5),(6,6)$)

Note: Make sure you consider all the favourable outcomes.

$P(E) = \frac{6}{{36}} = \frac{1}{6}$

$P(E) = \frac{6}{{36}} = \frac{1}{6}$

A single throw of dice can have $36$ i.e. $6 \times 6$ outcomes. So, let us take a look at all the $36$ outcomes.

$\left( {1,1} \right)\left( {1,2} \right)\left( {1,3} \right)\left( {1,4} \right)\left( {1,5} \right)\left( {1,6} \right)$

$\left( {2,1} \right)\left( {2,2} \right)\left( {2,3} \right)\left( {2,4} \right)\left( {2,5} \right)\left( {2,6} \right)$

$\left( {3,1} \right)\left( {3,2} \right)\left( {3,3} \right)\left( {3,4} \right)\left( {3,5} \right)\left( {3,6} \right)$

$\left( {4,1} \right)\left( {4,2} \right)\left( {4,3} \right)\left( {4,4} \right)\left( {4,5} \right)\left( {4,6} \right)$

$\left( {5,1} \right)\left( {5,2} \right)\left( {5,3} \right)\left( {5,4} \right)\left( {5,5} \right)\left( {5,6} \right)$

$\left( {6,1} \right)\left( {6,2} \right)\left( {6,3} \right)\left( {6,4} \right)\left( {6,5} \right)\left( {6,6} \right)$

Now, it is given that the total on the dice of $A$ is $9$.

Let E be the event of getting a number on $B$’s dice that is greater than $9$

Number of favourable outcomes= $6$(i.e.$(4,6),(5,5),(5,6),(6,4),(6,5),(6,6)$)

Note: Make sure you consider all the favourable outcomes.

$P(E) = \frac{6}{{36}} = \frac{1}{6}$

$P(E) = \frac{6}{{36}} = \frac{1}{6}$

Recently Updated Pages

If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

The coordinates of the points A and B are a0 and a0 class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write the 6 fundamental rights of India and explain in detail

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Name the 8 union territories of India

What are merits and demerits of democracy

Define human made resources

What is pollution? How many types of pollution? Define it

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

1 million is equivalent to which of the following -class-6-maths-CBSE