Answer

Verified

407.7k+ views

Hint- Here, we will be using the general formula for probability i.e., Probability of occurrence of an event$ = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of possible outcomes}}}}$ in order to find the required probability.

Given that we are tossing four coins and we have to find out the probability of obtaining two heads and two tails.

According to general formula for probability of occurrence of an event, we can write

Probability of occurrence of an event$ = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of possible outcomes}}}}$

By tossing four coins, the possible outcomes are (H,H,H,H), (T,H,H,H), (H,T,H,H), (H,H,T,H), (H,H,H,T), (T,T,H,H), (T,H,T,H), (T,H,H,T), (H,T,T,H), (H,T,H,T), (H,H,T,T), (T,T,T,H), (T,T,H,T), (T,H,T,T), (H,T,T,T), (T,T,T,T) where H represents occurrence of head while tossing a coin and T represents occurrence of tail while tossing a coin.

Therefore, Total number of possible outcomes = 16

Here, the favourable event is getting two heads and two tails on tossing four coins.

Clearly, the favourable outcomes after tossing four coins are (T,T,H,H), (T,H,T,H), (T,H,H,T), (H,T,T,H), (H,T,H,T) and (H,H,T,T).

Therefore, Number of favourable outcomes = 6

Probability of obtaining two heads and two tails $ = \dfrac{{\text{6}}}{{{\text{16}}}} = \dfrac{3}{8}$.

Hence, the chance that there should be two heads and two tails after tossing four coins is $\dfrac{3}{8}$.

Note- In these types of problems, where tossing of n coins is associated we already have a formula for calculating the total number of possible cases that will occur when n coins are tossed. i.e., Total number of possible outcomes when n coins are tossed =${2^{\text{n}}}$ (in this case n=4 that’s why total number of possible outcomes =${2^4} = 16$).

Given that we are tossing four coins and we have to find out the probability of obtaining two heads and two tails.

According to general formula for probability of occurrence of an event, we can write

Probability of occurrence of an event$ = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of possible outcomes}}}}$

By tossing four coins, the possible outcomes are (H,H,H,H), (T,H,H,H), (H,T,H,H), (H,H,T,H), (H,H,H,T), (T,T,H,H), (T,H,T,H), (T,H,H,T), (H,T,T,H), (H,T,H,T), (H,H,T,T), (T,T,T,H), (T,T,H,T), (T,H,T,T), (H,T,T,T), (T,T,T,T) where H represents occurrence of head while tossing a coin and T represents occurrence of tail while tossing a coin.

Therefore, Total number of possible outcomes = 16

Here, the favourable event is getting two heads and two tails on tossing four coins.

Clearly, the favourable outcomes after tossing four coins are (T,T,H,H), (T,H,T,H), (T,H,H,T), (H,T,T,H), (H,T,H,T) and (H,H,T,T).

Therefore, Number of favourable outcomes = 6

Probability of obtaining two heads and two tails $ = \dfrac{{\text{6}}}{{{\text{16}}}} = \dfrac{3}{8}$.

Hence, the chance that there should be two heads and two tails after tossing four coins is $\dfrac{3}{8}$.

Note- In these types of problems, where tossing of n coins is associated we already have a formula for calculating the total number of possible cases that will occur when n coins are tossed. i.e., Total number of possible outcomes when n coins are tossed =${2^{\text{n}}}$ (in this case n=4 that’s why total number of possible outcomes =${2^4} = 16$).

Recently Updated Pages

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

What is the stopping potential when the metal with class 12 physics JEE_Main

The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main

Basicity of sulphurous acid and sulphuric acid are

Using the following information to help you answer class 12 chemistry CBSE

Why should electric field lines never cross each other class 12 physics CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a book review which you have recently read in class 8 english CBSE

Difference Between Plant Cell and Animal Cell

Describe the poetic devices used in the poem Aunt Jennifers class 12 english CBSE

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

State the laws of reflection of light

What I want should not be confused with total inactivity class 12 english CBSE