$A$ 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 $A$ .
Answer
365.4k+ 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.
$P(E) = \frac{6}{{36}} = \frac{1}{6}$
$P(E) = \frac{6}{{36}} = \frac{1}{6}$
Last updated date: 29th Sep 2023
•
Total views: 365.4k
•
Views today: 9.65k
Recently Updated Pages
What do you mean by public facilities

Please Write an Essay on Disaster Management

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

One cusec is equal to how many liters class 8 maths CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

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.

How many millions make a billion class 6 maths CBSE

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

How many crores make 10 million class 7 maths CBSE
