If a biased coin is tossed 3 times the probability of getting 2 heads and 1 tail is equal to the probability of getting 3 heads. Find the probability of getting 4 heads when it is tossed 4 times. Pls. explain the solution to this Qn.

Hi
One thing in probability you have to keep in mind is the sum of all probabilities is always 1 irrespective of whether we have biased or unbiased.
Now let probability of Head be P now a coin has only two outcomes so the probability of other outcome will be 1-p
so probability of Tail is 1-p
Now probability of 2 heads when tossed 3 times will be 3C2 P^2(1-P) (Third one will be tail )
Getting 3 heads = 3C3 P^3
Equating we get 3p^2(1-p)=p^3
solving we get p=3/4
Now probability when tossed 4 times to get 4 heads will be :
4C4P^4=P^4=81/256

Thank you!