SOLUTION: * Show your complete solution * Explain your answer after the solution A coin is tossed three times. What is the probability of getting a. A head on the first toss b. A head o

Let "H" codes head and "T" codes tail.

Each event/outcome of three tosses we will present as a word of the length 3 of letters H and T.

For example, the outcome "Head, Head, Tail" is the word HHT;

             the outcome "Tail, Head, Tail" is the word THT.


Then the full space of events is the set of 8 possible outcomes, presented by words in this table


   1   HHH
   2   HHT
   3   HTH
   4   HTT
   5   THH
   6   THT
   7   TTH
   8   TTT


As you see, there are 8 events in this space of events.

Now I will answer the questions.


(a) Probability "a head on the first toss."


    Look at the table.

    H in first position is in 4 events: nn. 1,2,3,4.

    THEREFORE, the answer to question (a) is  P = 1/4 = 0.25 = 25%.



(b) Probability "a head on the second toss given that it is a head on the first toss."


    A head on the first toss is in four events nn.1,2,3,4.

    Of them, events with the head on the second toss is in two events nn. 1,2.

    THEREFORE, the answer to question (b) is  P = 2/4 = 1/2 = 0.5 = 50%.



(c) Probability "A head on the third toss given that it is a head on the first two tosses."


    A head on the first two tosses is in two events nn.1,2.

    Of them, events with the head on the first toss is in only one event n. 1.

    THEREFORE, the answer to question (c) is  P = 1/2 = 0.5 = 50%.