Question on probability?

Question

A coin is tossed three times. The probability of getting heads is .3 and tails is .7

What is the probability of resulting in

a) three consecutive tails?
b) two heads, one tail?
c) two tails, one head?

Answer 1

a) three consecutive tails?
p(3 tails) = 0.7³ = 0.343

b) two heads, one tail?
p(2 heads and 1 tail) = 3*(0.3²)(0.7) = 0.189

b) two tails, one head?
p(2 tails and 1 head) = 3*(0.7²)(0.3) = 0.441

Answer 2

Probability of more than one thing you multiply the individual probabilities together ..

a) 0.7 times 0.7 times 0.7 = 0.343
b) 0.3 times 0.3 times 0.7 = 0.063
c) 0.7 times 0.7 times 0.3 = 0.147

Answer 3

(a) 0.7 * 0.7 * 0.7 = 0.343
(b) 0.3 * 0.3 * 0.7 = 0.063 in order head, head, tail
also 0.3 * 0.7 * 0.3 of head, tail, head in that order
and 0.7 * 0.3 * 0.3 of tail, head, head in that order
therefore 3 * 0.063 = 0.189
(c) similarly to (b) 3 * 0.3 * 0.7 * 0.7 = 0.441