Question

A coin is weighted so that there is a 61% chance that it will come up "heads" when flipped.

The coin is flipped four times. Find the probability of getting two "heads" and two "tails".

Please explain each step in detail

Answer 1

Solution:

We are given

n = number of trials = 4

p = probability of success = 61% = 0.61

For this experiment, all trials are independent and all outcomes are binomial (head or tail).

So, we have to use binomial distribution. We have to find probability of getting two "heads" and two "tails", this means we have to find the probability of getting exact two heads.

We have to find P(X = two heads) = P(X=2)

P(X=x) = nCx*p^x*q^(n – x)

q = 1 – p = 1 – 0.61 = 0.39

P(X=2) = 4C2*0.61^2*0.39^(4 – 2)

P(X=2) = 6*0.61^2*0.39^2

P(X=2) = 0.339578

Required probability = 0.3396