An unfair coin is tossed three times. For each toss, the probability that the coin comes up heads is 0.4 and the probability that the coin comes up tails is 0.6

if we let X be the number of coin tosses that come up heads, observe that the possible values of X are 0, 1, 2, and 3. Find the probability distribution of X

Hint: the problem can be solved in two different ways as describe below. Both methods will result in the same answer.

Method 1: write out the sample space of possible outcomes, obtain the probability of each of the outcomes and relate each of these outcomes to X= 0, X=1, X=2, X=3.

Method 2: Verify that the four requirements of the binomial setting are satisfied in this problem. Use the Binomial formula fo each possible value of X to obtain the probability distribution of X.

what is P(X=0)? round answer to 3 decimal places

what is P(X=1)? round answer to 3 decimal places

What is P(X=2)? round answer to 3 decimal places

what is P(X=3) ?round answer to 3 decimal places