Consider an experiment of flipping a fair coin 50 times. Assign a random variable x, where the value of x is e

Question

Consider an experiment of flipping a fair coin 50 times. Assign a random variable x, where the value of x is equal to the number of heads observed in the flips. Describe the probability distribution of x, and calculate the probability of observing 30 or more heads or more in 50 flips.

Answer 1

Using the binomial distribution as James L did only works well answering questions like calculate P(n=30). (exactly 30 heads)

For answering a question like calculate P(n>=30) the normal approximation of the binomial distribution is used:
The binomial distribution is approximated by a normal distribution
N(mu,sigma)
with mu = average value = 25
sigma = standard deviation = sqrt (50x0.5x(1-0.5)) = 3.54

now: P(n>=30) = P (x>29,5) = P(z>1.27) = 0.3980

where the z-score was calculated from z = (29.5-25)/3.54
and the probabilities for this z-scores was found in the table below.

Answer 2

Each flip is a Bernoulli trial. Since the coin is fair (probability of heads = 0.5), it follows that the probability of k heads in n trials is

C(n,k)(0.5)^k (0.5)^(n-k)

where C(n,k)=n!/[k!(n-k)!] is the binomial coefficient "n-choose-k".

This is known as the binomial distribution.

To find the probability of 30 heads in 50 flips, let n=50 and k=30. You get

C(50,30)0.5^30 * 0.5^20 = 0.041859.

Answer 3

Do your own homework