Answer

Verified

439.8k+ views

**Hint:**To solve this problem we need to find the favorable cases for the given numbers.Here we have to find the favourable cases for both prime numbers and multiples of 4.

Required formula

Probability of event to happen \[P(E)\]

\[ = \dfrac{{Number\,of\,favourable\,outcome}}{{total\,number\,of\,outcomes}}\]

**Complete step-by- step solution:**

Given that,

A bag contain ticket numbered from 1 to 20

The two tickets are drawn

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

Now, prime numbers are the numbers that have only two factors i.e. 1 and itself.

Here prime numbers are - 1 2 3 5 7 11 13 17 i.e. 8 favorable cases.

Here multiples of 4 are\[ \to \] 4, 8, 12, 16, 20 i.e. 5 favorable cases

Total numbers \[ = 20\]

Now probability of prime number \[ = \dfrac{{Number\,of\,favourable\,outcome}}{{total\,number\,of\,outcomes}}\]\[ = \dfrac{8}{{20}}\]

Probability of multiple of 4 \[ =\dfrac{{Number\,of\,favourable\,outcome}}{{total\,number\,of\,outcomes}}\]\[ = \dfrac{5}{{20}}\]

We need to find Probability (one there is a prime number and other there is a multiple of\[4\])

\[ = \dfrac{8}{{20}} \times \dfrac{5}{{19}} + \dfrac{5}{{20}} \times \dfrac{8}{{19}}\]

\[ = \dfrac{{40 + 40}}{{20 \times 19}} = \dfrac{{80}}{{20 \times 19}} = \dfrac{4}{{19}}\]

Probability (one there is prime number and another is multiple of\[4\])

\[ = \dfrac{4}{{19}}\]

**Note:**Probability means possibility.

We must remember that when we have picked one number out of 20 then while picking the second number from the same, the total possibilities will be 19.

We need to remember that in probability we use multiplication until the case is completed but we use addition when the case has been completed and it is ‘either or case’.

We use the basic concept of probability.

Recently Updated Pages

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

Advantages and disadvantages of science

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

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

10 examples of evaporation in daily life with explanations

Difference Between Plant Cell and Animal Cell

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

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