# Two dice are thrown simultaneously. What is the probability that:

(i) 5 will not come upon either of them

(ii) 5 will come upon at least one

(iii) 5 will come up at both the dice

Last updated date: 26th Mar 2023

•

Total views: 312k

•

Views today: 2.89k

Answer

Verified

312k+ views

Hint: Use probability=favorable cases/ total cases.

In a throw of pair of dice, total no of possible outcomes $ = 36\left( {6 \times 6} \right)$ which are:

$

\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) \\

$

(i) Let $E$ be the event of not getting a 5 on either of the two dice

Number of favorable outcomes=25

Total number of outcomes=36

$P\left( E \right) = \dfrac{{25}}{{36}}$

(ii) Let $E$ be the event of getting a 5 at least once

Number of favorable outcomes=11

Total number of outcomes=36

$P\left( E \right) = \dfrac{{11}}{{36}}$

(iii) Let $E$ be the event of getting a 5 on both dice

Number of favorable outcomes=1

Total number of outcomes=36

$P\left( E \right) = \dfrac{1}{{36}}$

Note: In the above solution the table made at the top containing the list of all possible outcomes is known as sample space of the event. In all the three parts of the solution, a number of favorable outcomes has been found out after counting the same from the above table.

In a throw of pair of dice, total no of possible outcomes $ = 36\left( {6 \times 6} \right)$ which are:

$

\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) \\

$

(i) Let $E$ be the event of not getting a 5 on either of the two dice

Number of favorable outcomes=25

Total number of outcomes=36

$P\left( E \right) = \dfrac{{25}}{{36}}$

(ii) Let $E$ be the event of getting a 5 at least once

Number of favorable outcomes=11

Total number of outcomes=36

$P\left( E \right) = \dfrac{{11}}{{36}}$

(iii) Let $E$ be the event of getting a 5 on both dice

Number of favorable outcomes=1

Total number of outcomes=36

$P\left( E \right) = \dfrac{1}{{36}}$

Note: In the above solution the table made at the top containing the list of all possible outcomes is known as sample space of the event. In all the three parts of the solution, a number of favorable outcomes has been found out after counting the same from the above table.

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

KCN reacts readily to give a cyanide with A Ethyl alcohol class 12 chemistry JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?