Coin toss probability

Question

A fair coin is tossed 12 times. What is the probability of obtaining heads exactly once? Express the answer in both tera of nCk and as a four-place decimal.

Answer 1

According to the Binomial Probability formula, 

 

P(k successes in n trials) = (_nC_k)p^kq^n-k

 

p = probability of success on a given trial = probability that a given toss of the coin is heads = .5

 

q = probability of failure on a given trial = probability that a given toss is tails = .5

 

n = number of trials = number of tosses = 12

 

k  = number of successes in n trials = number of tosses that came up heads = 1

 

So, P(1 head in 12 tosses) = ₁₂C₁(.5)¹(.5)¹¹

 

                                           ≈ 0.0029