Answer to Question #129740 in Statistics and Probability for souvik Biswas

Question

a coin is tossed 4 times what is probability of obtaining 3 heads if it is known that a head has been obtained as the first toss

Answer 1

In this case, we have been given that out of 4 tosses the first toss is a head.

So now we need to obtain 2 more heads in the remaining 3 tosses.

The number of heads can be modeled as a binomial distribution.

Assuming that the coin is fair the probability of getting a head, p = 0.5.

Thus number of remaining tosses, n = 3

We want probability that X = 2 (X being the random variable denoting the number of heads obtained in the experiment)

We know that , if X~Bin(n,p), then P(X = x) = (nCx).p^x(1-p)^(n-x)

$\therefore P(X = 2) =(3C2)*(0.5)^2*(1-0.5)^{(3-2)}$

$\therefore P(X = 2) = 0.375$