im having trouble

Question

Say you have a biased coin and you associate obtaining a head with the value 0 whereas obtaining a tail has a value of 2. Let X be the sum of the values obtained from tossing the coin three times. (Round your answers to 4 decimal places, if needed.)

(a) If the probability of getting heads in a single toss is 0.38, then what is the probability distribution of X ?

x	0	2	4	6
P(X = x)

(b) What is P(X < 6)?

(c) What is P(1 < X < 5)?

Answer 1

P(X<6)= 1-P(X=6)

P(X=6) = Probability of 3 heads in 3 flips

= .38^3 = 0.054872 = 5.4872%

P(X<6) = 100%-5.4872%

= 94.5128%

= about 95%