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  1. Describe in words the events specified by the following subsets of

= {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} (see Example 1.6).

  1. E = {HHH,HHT,HTH,HTT}.
  2. E = {HHH,TTT}.
  3. E = {HHT,HTH,THH}.
  4. E = {HHT,HTH,HTT,THH,THT,TTH,TTT}.

Answer:

  1. E = {HHH,HHT,HTH,HTT}. Here,

This subset represents the outcomes of the first toss being the head followed by either heads or tails.

  1. E = {HHH,TTT}. Here,

This subset represents the outcomes of either all the outcomes are head or tails. There is no mixtrues of head and tails in this subset.

  1. E = {HHT,HTH,THH}. Here,

This subset represents the outcomes of three different options in which at first the tossed coins outcomes should be in the sequence of tail being the last option then in second toss the tail should be the second outcome and in the third toss the outcome of tail should be the first option.

  1. E = {HHT,HTH,HTT,THH,THT,TTH,TTT}. Here,

This outcome subset represents exact similar to the universal subset except the toss when there are all head outcomes.