Question

A coin is loaded so that the probability of occurrence of a face is 3 times that of a cross. Calculate the variance of the number of crosses if this coin is tossed twice.

Answer with up to 4 decimals.

Answer 1

A coin is tossed, there are two chances one is face and other is cross.

Let probability of occurrence cross comes is = p then

probability of occurrence of face is 3 times that of cross = 3p

Now we know that sum of all probabilities must be 1

p+3p = 1

4p = 1

p= 1/4

Probability of occurrence of cross = p = 1/4 = 0.26

Coin tosses twice , n= 2

Let X is random variable such that after tossing coin face comes or cross comes with probability of occurrence of crosses is 1/4

X follows Binomial Distribution

X ~ Binomial(n=2, p= 0.25)

We know variance of Binomial Distribution is given by

Varianceof X = Var(X) = np(1-p) = 2*0.25*(1-0.25)

Var(X) = 0.3750

Variance of number of crosses if this coin tosses twice is 0.3750