Answer

Verified

479.1k+ views

Hint- Write samples of cases of total favorable and that of event to reach up to the probability.

If we toss two different dice than, total favorable cases are

$S = \left[ \begin{gathered}

\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( {6,5} \right),\left( {6,6} \right) \\

\end{gathered} \right]$

Thus $n(S) = 36$

Now the favorable outcome to get product of 6 are

$\left[ {\left( {1,6} \right),\left( {6,1} \right),\left( {2,3} \right),\left( {3,2} \right)} \right]$

Thus let E be an event of getting a product 6 on toss of two dice then $n(E) = 4$

Now $P(E) = \dfrac{{Favorable{\text{ cases of event E}}}}{{Total{\text{ possible sample cases}}}} = \dfrac{{n(E)}}{{n(S)}}$……………………………. (1)

Using equation (1)

$P(E) = \dfrac{4}{{36}} = \dfrac{1}{9}$

Hence probability of getting a product 6 while toss of two different dice is $\dfrac{1}{9}$

Note- Whenever we have to solve such type of problems always write down the set of all possible sample cases and then the cases corresponding to that particular event, this helps in reducing the chances of leaving any sample case .Then use the probability basics of $P(E) = \dfrac{{Favorable{\text{ cases of event E}}}}{{Total{\text{ possible sample cases}}}} = \dfrac{{n(E)}}{{n(S)}}$to reach to the solution.

If we toss two different dice than, total favorable cases are

$S = \left[ \begin{gathered}

\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( {6,5} \right),\left( {6,6} \right) \\

\end{gathered} \right]$

Thus $n(S) = 36$

Now the favorable outcome to get product of 6 are

$\left[ {\left( {1,6} \right),\left( {6,1} \right),\left( {2,3} \right),\left( {3,2} \right)} \right]$

Thus let E be an event of getting a product 6 on toss of two dice then $n(E) = 4$

Now $P(E) = \dfrac{{Favorable{\text{ cases of event E}}}}{{Total{\text{ possible sample cases}}}} = \dfrac{{n(E)}}{{n(S)}}$……………………………. (1)

Using equation (1)

$P(E) = \dfrac{4}{{36}} = \dfrac{1}{9}$

Hence probability of getting a product 6 while toss of two different dice is $\dfrac{1}{9}$

Note- Whenever we have to solve such type of problems always write down the set of all possible sample cases and then the cases corresponding to that particular event, this helps in reducing the chances of leaving any sample case .Then use the probability basics of $P(E) = \dfrac{{Favorable{\text{ cases of event E}}}}{{Total{\text{ possible sample cases}}}} = \dfrac{{n(E)}}{{n(S)}}$to reach to the solution.

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

Which are the Top 10 Largest Countries of the World?

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How do you graph the function fx 4x class 9 maths CBSE

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

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

What organs are located on the left side of your body class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell