Answer :

Say, H represents event of getting a head and T represents getting a tail.

When we toss a coin 4 times we have the following possibilities:


A total of 24 = 16 possibilities.

Let X be a random variable representing number of heads occuring in 4 tosses of a coin.

probability of getting a head or probability of getting a tail are independent events and P(GETTING A HEAD) = P(GETTING A TAIL) = 1/2

P(Head in first toss) and P(Head in second toss) and P(head in third toss) and P(tail in 4th toss) can be given by their individual products.

Note: P(AՈB) = P(A)P(B) where A and B are independent events.


P(X=0) = P(TTTT) = P(T)P(T)P(T)P(T) = 1/2 x 1/2 x 1/2 x 1/2 = 1/16

Selecting a coin out of 4 which will show head rest all showing tail

P(X=1) =


P(X=2) =

P(X=3) =

P(X=4) = P(HHHH) = 1/16

Now we have pi and xi.

Let’s proceed to find mean and variance.

Mean of any probability distribution is given by Mean = ∑xipi

Variance is given by:

Variance = ∑ xi2pi – (∑xipi)2

first we need to find the products i.e. pixi and pixi2 and add them to get mean and apply the above formula to get the variance.

Following table representing probability distribution gives the required products :

Mean =

Variance =

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