Answer

Verified

429.9k+ views

**Hint:**Probability may be simply defined as the chance of happening of a certain event.

For an event, there might be many possible outcomes. Probability is the chance of any event to take place.

Here we will use the formula of probability which states that

\[{\text{Probability of an event}} = \dfrac{{{\text{No of favourable outcomes}}}}{{{\text{Total Outcomes}}}}\]

In case of dice, throwing two or three dices simultaneously can be treated as throwing a single dice two or three times.

Here we will use the cases of dice, whose formula is \[{6^n}\] where n is the number of times the dice has been thrown.

**Complete step-by-step answer:**

Firstly, we will discuss the case of throwing one die.

When one die is thrown, \[n = 1\]

\[ \Rightarrow Total{\text{ }}number{\text{ }}of{\text{ }}outcomes = {6^1} = 6\]

Out of these, only one is 4.

So, \[Favourable{\text{ }}Outcomes = 1\]

\[{\text{The probability of getting 4}} = \dfrac{{{\text{No of favourable outcomes}}}}{{{\text{Total Outcomes}}}}\]

\[ \Rightarrow P(4) = \dfrac{1}{6}\]

**The probability of getting 4 with one die is \[\dfrac{1}{6}\]**

Now, we will discuss the case of throwing two dice.

When two dice are thrown, \[n = 2\]

\[ \Rightarrow Total{\text{ }}number{\text{ }}of{\text{ }}outcomes = {6^2} = 36\]

Out of these, we get 8 in only these cases \[ = \left\{ {\left( {2,{\text{ }}6} \right),\left( {3,{\text{ }}5} \right),\left( {4,{\text{ }}4} \right),\left( {5,{\text{ }}3} \right),\left( {6,{\text{ }}2} \right)} \right\}\]

So, \[Favourable{\text{ }}Outcomes = 5\]

\[{\text{The probability of getting 8 on 2 dice}} = \dfrac{{{\text{No of favourable outcomes}}}}{{{\text{Total Outcomes}}}}\]

\[ \Rightarrow P(8{\text{ }}on{\text{ }}2{\text{ }}dice) = \dfrac{5}{{36}}\]

**The probability of getting a sum of 8 with 2 die is \[\dfrac{5}{{36}}\]**

Now, we will discuss the case of throwing three dice.

When three dice are thrown, \[n = 3\]

\[ \Rightarrow Total{\text{ }}number{\text{ }}of{\text{ }}outcomes = {6^3} = 216\]

Out of these, we get 12 in only these cases = \[

\{ (1,5,6),(1,6,5),(5,1,6),(5,6,1),(6,1,5), \\

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

(6,2,4),(6,4,2),(2,5,5),(5,2,5),(5,5,2), \\

(3,3,6),(3,6,3),(6,3,3),(3,5,4),(3,4,5), \\

(4,3,5),(4,5,3),(5,3,4),(5,4,3),(4,4,4)\} \\

\]

So, \[Favourable{\text{ }}Outcomes = 25\]

\[{\text{The probability of getting 12 on 3 dice}} = \dfrac{{{\text{No of favourable outcomes}}}}{{{\text{Total Outcomes}}}}\]

\[ \Rightarrow P(12{\text{ }}on{\text{ 3 }}dice) = \dfrac{{25}}{{216}}\]

**The probability of getting a sum of 12 with 3 dies is \[\dfrac{25}{{216}}\]**

**Note:**Some additional information about probability is as follows:

The sum of probabilities of all the events of an experiment is always equal to 1.

Probability can have minimum value 0 and maximum value 1.

If the sum of probabilities of an experiment is either less than 0 or greater than 1, then there is a mistake in the calculation.

Probability of an event which is which will definitely take place is 1. Such an event is called a True event.

Probability of an event which has not taken place is always taken as 0. Such an event is called False event

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

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

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

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

10 examples of evaporation in daily life with explanations

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE