Answer

Verified

412.8k+ views

**Hint:**Here first we will find all the two digit numbers which can be formed using the given digits and write the sample space and also write the number of elements in sample space.Then we will list all the numbers which are divisible by 5 from the numbers listed in sample space S and write then in U and also write the number of elements in U so formed.A number is divisible by 5 if its unit’s place contains 0 or 5.

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

The given digits are:-

0,1,2,3,4,5

Now since we know that no two digit number can start with 0 hence we will first list all the numbers starting with 1:

10, 11, 12,13,14,15

Now, we will list all the numbers starting with 2:-

20, 21, 22,23,24,25

Now, we will list all the numbers starting with 3:-

30, 31, 32,33,34,35

Now, we will list all the numbers starting with 4:-

40, 41, 42,43,44,45

Now, we will list all the numbers starting with 5:-

50, 51, 52,53,54,55

Therefore the sample space S is given by:-

\[S = \left\{ {10,{\text{ }}11,{\text{ }}12,13,14,15,20,{\text{ }}21,{\text{ }}22,23,24,25,30,{\text{ }}31,{\text{ }}32,33,34,35,40,{\text{ }}41,{\text{ }}42,43,44,45,50,{\text{ }}51,{\text{ }}52,53,54,55} \right\}\]

Now counting the number of elements in S we get:-

\[n\left( S \right) = 25\]

Now since we know that a number is divisible by 5 if its unit’s place contains 0 or 5.

Hence listing such numbers from S which have 0 or 5 at unit’s place we get:-

10,15,20,25,30,35,35,40,45,50,55

Since the U is the event that it contains the number which is divisible by 5

Hence, U is given by:-

\[U = \left\{ {10,15,20,25,30,35,35,40,45,50,55} \right\}\]

Now counting the number of elements in U we get:-

\[n\left( U \right) = 11\]

Therefore,

Sample space S is:

\[S = \left\{ {10,{\text{ }}11,{\text{ }}12,13,14,15,20,{\text{ }}21,{\text{ }}22,23,24,25,30,{\text{ }}31,{\text{ }}32,33,34,35,40,{\text{ }}41,{\text{ }}42,43,44,45,50,{\text{ }}51,{\text{ }}52,53,54,55} \right\}\]

Number of elements in S are:-

\[n\left( S \right) = 25\]

The event U is:-

\[U = \left\{ {10,15,20,25,30,35,35,40,45,50,55} \right\}\]

Number of elements in U are:-

\[n\left( U \right) = 11\].

**Note:**Students should note that a number is divisible by 5 if and only if its unit’s place contains 0 or 5, all other numbers are not divisible by 5.Also in such questions, it is advised to write the whole sample space first i.e. writing all the possible outcomes according to the given condition.

Recently Updated Pages

The base of a right prism is a pentagon whose sides class 10 maths CBSE

A die is thrown Find the probability that the number class 10 maths CBSE

A mans age is six times the age of his son In six years class 10 maths CBSE

A started a business with Rs 21000 and is joined afterwards class 10 maths CBSE

Aasifbhai bought a refrigerator at Rs 10000 After some class 10 maths CBSE

Give a brief history of the mathematician Pythagoras class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Name 10 Living and Non living things class 9 biology CBSE

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

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail