Question 997817: A fair coin is flipped ten times. What is the probability of the coin landing heads up exactly six times? Answer by mathmate(429) (Show Source):
Need:
Probability of heads coming up exactly six times.
Solution:
Typical use of the binomial distribution where:
- probability (1/2) is constant throughout experiement
- multi-step Bernoulli experiement (each with two possible outcomes)
- all steps are independent of each other and random.
events and probability for each trial:
H=heads, P(H)=1/2
T=tails, P(T)=1/2
p, P(H) = probability of heads as outcome in each trial
Probability of exactly r events out of n is given by the binomial formula:
In the given situation, n=10, r=6, p=1/2, nCr=10C6=10!/(6!4!)=210
so P(6,10,1/2)=(210)* ((1/2)^6) * ((1-1/2)^4) =210/1024 = 105/512
Answer:
Probability of getting exactly 6 heads out of ten tosses of a fair coin is 105/512.
