Answer

Verified

394.2k+ 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.

Recently Updated Pages

How do you find slope point slope slope intercept standard class 12 maths CBSE

How do you find B1 We know that B2B+2I3 class 12 maths CBSE

How do you integrate int dfracxsqrt x2 + 9 dx class 12 maths CBSE

How do you integrate int left dfracx2 1x + 1 right class 12 maths CBSE

How do you find the critical points of yx2sin x on class 12 maths CBSE

How do you find the general solution to dfracdydx class 12 maths CBSE

Trending doubts

The provincial president of the constituent assembly class 11 social science CBSE

Gersoppa waterfall is located in AGuyana BUganda C class 9 social science CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The hundru falls is in A Chota Nagpur Plateau B Calcutta class 8 social science CBSE

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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