A biased coin is flipped 20 times in a row. The coin has a probability 0.75...

A biased coin is flipped 20 times in a row. The coin has a probability 0.75 of showing Heads.

a. What’s the probability that you get exactly 8 Heads?

b. What’s the probability that you get exactly 8 Heads, given that the first 2 flips show Heads?

c. What’s the probability that you never see the same result consecutively( never see 2H or 2T in a row)

Solutions

Expert Solution

a) The probability that there are exactly 8 heads is computed using the binomial probabiltiy function as:

Therefore 0.000752 is the required probability here.

b) Probability that we get exactly 8 Heads, given that the first 2 flips show Heads

= Probability that there are exactly 6 heads in the next 18 tosses, as there were already 2 heads in the first 2 tosses

Therefore 0.000197 is the required probability here.

c) The probability that you never see the same result consecutively is computed here as:

= P(HTHTHTH....) + P(THTHTHTH....)

= 2*0.520 = 0.519

Therefore 0.519 is the required probability here.

orchestra answered 1 year ago

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