Example on Discrete Unifrom Probability | MIT Assignment

You flip a fair coin 3 times, determine the probability of the below events. Assume all sequences are equally likely.

A) Three heads: HHH

B) The sequence head, tail, head: HTH

C) Any sequence with 2 heads and 1 tail

D) Any sequence where the number of heads is greater than or equal to the number of tails

Answer

Since all outcomes are equally likely we apply the discrete uniform probability law to solve the problem. To solve for any event we simply count the number of elements in the event and divide by the total number of elements in the sample space.

There are 2 possible outcomes for each flip, and 3 flips. Thus there are 23 = 8 elements (or sequences) in the sample space.

A) Any sequence has probability of 1/8. Therefore P({H, H, H}) = 1/8 .

B) This is still a single sequence, thus P({H, T, H}) = 1/8 .

C) The event of interest has 3 unique sequences, thus P({HHT, HTH, THH}) = 3/8 .

D) The sequences where there are more heads than tails are

A : {HHH, HHT, HTH, THH}.

4 unique sequences gives us P(A) = 1/2 .

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