Answer
417.9k+ views
Hint: According to the basic definition of probability, probability of occurrence of any event is the ratio of the number of elements in the event to the total number of possible elements. Find the event in the above question. Find the total number of elements. And then use the formula of basic theorem of probability.
Complete step-by-step answer:
Let us say that $ S $ is a sample space of all possible outcomes. And $ n(S) $ is the total number of possible outcomes.
Let us say that $ E $ is an event will possible outcomes of that event. And $ n(E) $ is the total number of possible outcomes of that event.
Then, according to the basic theorem of probability, the probability of occurrence of an element in the said event is given by $ P(E) $ .
Where,
$ P(E) = \dfrac{{n(E)}}{{n(S)}} $ . . . (1)
Sample space for this question will be the collection of cards from 1 to 30. i.e.
$ S = \{ 1,2,3....,30\} $
$ \Rightarrow n(S) = 30 $
(i) a multiple of 4 or 6
For this, the event can be written as
$ E = \{ 4,6,8,12,16,18,20,24,28,30\} $
$ \Rightarrow n(E) = 10 $
Therefore, from equation (1), we get
$ P(E) = \dfrac{{10}}{{30}} = \dfrac{1}{3} $
Thus, the probability of getting a card which is a multiple of 4 or 6 is $ \dfrac{1}{3} $
So, the correct answer is “ $ \dfrac{1}{{3}} $ ”.
(ii) a multiple of 3 and 5
For this, the event can be written as
$ E = \{ 15,30\} $
$ \Rightarrow n(E) = 2 $
Therefore, from equation (1), we get
$ P(E) = \dfrac{2}{{30}} = \dfrac{1}{{15}} $
Thus, the probability of getting a card which is a multiple of 3 and 5 is $ \dfrac{1}{{15}} $
So, the correct answer is “ $ \dfrac{1}{{15}} $ ”.
(iii) a multiple of 3 or 5
For this, the event can be written as
$ E = \{ 3,5,6,9,10,12,15,18,20,21,24,25,27,30\} $
$ \Rightarrow n(E) = 14 $
$ P(E) = \dfrac{{14}}{{30}} = \dfrac{7}{{15}} $
Thus, the probability of getting a card which is a multiple of 3 or 5 is $ \dfrac{7}{{15}} $
So, the correct answer is “ $ \dfrac{7}{{15}} $ ”.
Note: In this question, knowing the basic theorem of probability and knowing how to differentiate between an event and a sample space is important. Once you understand that and can find the number of elements in the event as well as in sample space. Then this question is about just substituting the values in the formula.
Complete step-by-step answer:
Let us say that $ S $ is a sample space of all possible outcomes. And $ n(S) $ is the total number of possible outcomes.
Let us say that $ E $ is an event will possible outcomes of that event. And $ n(E) $ is the total number of possible outcomes of that event.
Then, according to the basic theorem of probability, the probability of occurrence of an element in the said event is given by $ P(E) $ .
Where,
$ P(E) = \dfrac{{n(E)}}{{n(S)}} $ . . . (1)
Sample space for this question will be the collection of cards from 1 to 30. i.e.
$ S = \{ 1,2,3....,30\} $
$ \Rightarrow n(S) = 30 $
(i) a multiple of 4 or 6
For this, the event can be written as
$ E = \{ 4,6,8,12,16,18,20,24,28,30\} $
$ \Rightarrow n(E) = 10 $
Therefore, from equation (1), we get
$ P(E) = \dfrac{{10}}{{30}} = \dfrac{1}{3} $
Thus, the probability of getting a card which is a multiple of 4 or 6 is $ \dfrac{1}{3} $
So, the correct answer is “ $ \dfrac{1}{{3}} $ ”.
(ii) a multiple of 3 and 5
For this, the event can be written as
$ E = \{ 15,30\} $
$ \Rightarrow n(E) = 2 $
Therefore, from equation (1), we get
$ P(E) = \dfrac{2}{{30}} = \dfrac{1}{{15}} $
Thus, the probability of getting a card which is a multiple of 3 and 5 is $ \dfrac{1}{{15}} $
So, the correct answer is “ $ \dfrac{1}{{15}} $ ”.
(iii) a multiple of 3 or 5
For this, the event can be written as
$ E = \{ 3,5,6,9,10,12,15,18,20,21,24,25,27,30\} $
$ \Rightarrow n(E) = 14 $
$ P(E) = \dfrac{{14}}{{30}} = \dfrac{7}{{15}} $
Thus, the probability of getting a card which is a multiple of 3 or 5 is $ \dfrac{7}{{15}} $
So, the correct answer is “ $ \dfrac{7}{{15}} $ ”.
Note: In this question, knowing the basic theorem of probability and knowing how to differentiate between an event and a sample space is important. Once you understand that and can find the number of elements in the event as well as in sample space. Then this question is about just substituting the values in the formula.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)