Answer

Verified

413.4k+ views

**Hint:**First we toss a coin, it will give 2 outcomes. They are Head or tail,

Here we tossed a coin 3 times so it will give \[8\] outcomes. Now we find the possibilities of getting Event \[E\] and Event \[F\] and finally we find probability of \[E\] and \[F\].Here we use to find conditional probability, that is \[P\left( {\dfrac{E}{F}} \right) = \dfrac{{P(E \cap F)}}{{P(F)}}\] , if \[P(F) \ne 0\]

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

It is given that A coin is tossed three times in succession.

\[E\]: event that there are at least \[2\] heads.

\[F\]: event in which the first throw is head.

Total outcomes

1) H H H

2) H H T

3) H T H

4) T H H

5) T T H

6) T H T

7) H T T

8) T T T

After tossing a coin three times we get \[8\] outcomes

\[F\]: event in which the first throw is head

Total possibilities are \[4\]

H H T or H T H or H T T or H H H

The probability of the event F of getting head in the first trial is independent of the other \[2\] trails so it becomes

\[P(F) = \dfrac{4}{8} = \dfrac{1}{2}\]

\[E\]: event that there are at least \[2\] heads

\[2\] heads and \[1\] tail or \[3\] heads

Now we find \[P(E \cap F)\],

The probability that the \[3\] trails have at least \[2\] heads when the first thrown is a head we can find it

Total possibilities are \[3\]

H H T or H T H or H H H

\[P(E \cap F) = \dfrac{3}{8}\]

\[P(E/F) = \dfrac{{P(E \cap F)}}{{P(F)}}\]

\[P(E/F) = \dfrac{{3/8}}{{1/2}} = \dfrac{3}{4}\]

Therefore, \[P\left( {E/F} \right)\] is equal to \[\dfrac{3}{4}\].

**Note:**If we toss a coin once the probability of getting a head or tail will be the same \[ = \dfrac{1}{2}\].When we toss a coin n times, we will get the total number of outcomes \[ = {2^n}\]

Conditional Probability: If \[E\] and \[F\] are any two event in a sample space \[S\] and \[P(F) \ne 0\], then the conditional probability of given is, \[P\left( {\dfrac{E}{F}} \right) = \dfrac{{P(E \cap F)}}{{P(F)}}\].

Recently Updated Pages

What number is 20 of 400 class 8 maths CBSE

Which one of the following numbers is completely divisible class 8 maths CBSE

What number is 78 of 50 A 32 B 35 C 36 D 39 E 41 class 8 maths CBSE

How many integers are there between 10 and 2 and how class 8 maths CBSE

The 3 is what percent of 12 class 8 maths CBSE

Find the circumference of the circle having radius class 8 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

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

List some examples of Rabi and Kharif crops class 8 biology CBSE

Which are the Top 10 Largest Countries of the World?

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

Write the 6 fundamental rights of India and explain in detail