Question

a)  A coin is flipped 6 times, find the probability of getting exactly 4 heads.  Hint: The Binomial Distribution Table can be very helpful on questions 19-21.  If you use the table for this question, give your answer exactly as it appears.  If you calculated your answer, round to the thousandths place.

b) A coin is flipped 6 times. Find the probability of getting at least 3 heads. If you used a table to help find your answer, give it to the thousandths place. If you used a formula to calculate your answer, round to the thousandths place.

c) A coin is flipped 6 times, find the probability of getting at most 2 heads. If you used a table to help find your answer, give it to the thousandths place. If you used a formula to calculate your answer, round to the thousandths place.

Answer 1

Binomial Distribution

If 'X' is the random variable representing the number of successes, the probability of getting ‘r’ successes and ‘n-r’ failures, in 'n' trails, ‘p’ probability of success ‘q’=(1-p) is given by the probability function

For the given problem,

X : Number of heads got

Coin is flipped 6 tiems : Number of trails : n=6

Probability of getting a head : Probability of success : p = 1/2 =0.5

q = 1-p = 1-0.5 =0.5

X is a binomial distribution, with probability of getting 'r' heads

a) Probability of getting exactly 4 heads = P(X=4 )

Probability of getting exactly 4 heads = 0.234375

b) Probability of getting at least 3 heads = P(X3) = P(X=3)+P(X=4)+P(X=5)+P(X=6)

P(X3) = P(X=3)+P(X=4)+P(X=5)+P(X=6) = 0.3125+0.234375+0.09375+0.015625=0.65625

Probability of getting at least 3 heads = 0.65625

c) Probability of getting atmost 2 heads = P(X 2) = 1 - P(X 3)

From b) P(X3) = 0.65625

P(X 2) = 1 - P(X 3) = 0.65625 = 0.34375

Probability of getting atmost 2 heads = 0.34375