Question

An experiment consists of tossing a coin times and observing the sequence of heads and tails. ​(a) What is the sample space of this​ experiment? ​(b) Describe the event​ "the first toss is a ​" as a subset of the sample space.

Answer 1

Explanation:

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First you must know that a tossed coin can only produce a head (H) and a tail (T).

Sample space S1 = {H T}

When two coins are tossed, the possible outcomes are gotten by mapping another {H, T} to the previous sample space to have;

S2 = {HH, HT, TH, TT}

For three coin, the possible outcomes are gotten by mapping {H, T} to the previous sample space {HH, HT, TH, TT}to get S3

S3 = S1 × S2

S3 = {HHH, HHT HTH, HTT, THH, THT, TTH, TTT}

Hence the sample space of the experiment of tossing 3 coins is {HHH, HHT HTH, HTT, THH, THT, TTH, TTT}

n(S3) = 8

b) From the sample space, you can see that the event having the first toss as a tail are E = {THH, THT, TTH, TTT}

n(E) = 4