You flip a coin three times. (a) What is the probability of getting heads on only one of your flips? (b) What is the probability of getting heads on at least

Question

 

 Probability question

Answer 1

There are 8 possible outcomes. So the quickest way to calculate it is using the binomial distribution. 

 

P(X=k)= _nC_k p^k(1-p)^(n-k)

_nC_k denotes combination and is calculated as n!/[(n-k)!k!]

for a coin both p and (1-p) =.5

 

for part a we have n=3 and k=1

{3!/(2! 1!)} (.5)¹(.5)²

this simplifies to 3(.5)³ or 3/8 and that is the answer. 

 

You didn't finish part b but if you are looking for at least 1 time, you would calculate it by realizing that it is the

same as 1 - probability of getting it 0 times. Which can be shown using the method above as 1-1/8 or 7/8