Question

You are flipping a fair coin with one side heads, and the other tails. You flip it 30 times.

a) What probability distribution would the above most closely resemble?

b) If 8 out of 30 flips were heads, what is the probability of the next flip coming up heads?

c) What is the probability that out of 30 flips, not more than 15 come up heads?

d) What is the probability that at least 15 out 30 flips are heads? e) What is the probability that the 7 the flip is the first heads flip (6 tails then the head)?

Answer 1

(although there are more than 4 parts i will answer all , please UPVOTE)

a.

result of each coin flip is independent

therefore , it is a binomial distribution :

X=no. of heads

n=30 , p=0.5 , 1-p = 0.5

P(x) = 50Cx * (0.5^x) * (0.5^(50-x)) = 50Cx * 0.5^50

b.

each flip is independent

therefore,

P(heads in 9th flip) = 0.5

c.

probability that out of 30 flips, not more than 15 come up heads = P(x<=15)

= P(0)+P(1)+.....P(15) = 0.5722

P(x<=15) = 0.5722

d.

probability that at least 15 out 30 flips are heads = P(x>=15)

P(x>=15) = P(15)+P(16)+.....P(30)

= 0.5722

e.

probability that the 7 the flip is the first heads flip

= P(6 tails then the head)

= P(tails)^6 * P(heads)

= 0.5^6 * 0.5

probability that the 7 the flip is the first heads flip = 0.0078

P.S. (please upvote if you find the answer satisfactory)