A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample

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A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?​

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Mia 1 month 2021-08-16T15:56:15+00:00 2 Answers 0 views 0

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    0
    2021-08-16T15:57:56+00:00

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    \Large\fbox{\color{purple}{QUESTION}}

    A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?

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    \bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }

    ➡️Since either coin can turn up Head (H) or Tail (T), are the possible outcomes.

    ➡️Let us assume that 1, 2, 3, 4, 5 and 6 are the possible outcomes when the die is thrown.

    ➡️The problem can be solved by dividing it into 3 cases

    ➡️Case 1: The outcome is Head and the corresponding number on the die shows Odd number

    ➡️Total number of sample space = (1 × 3) = 3

    Total number of sample space = (1 × 3) = 3Sample space SHO = {(H,1), (H,3), (H,5)}

    ➡️Case 2: The outcome is Head and the corresponding number on the die shows Even number

    ➡️Total number of sample space = (1 × 3 × 6) = 18

    ➡️SHE={(H,2,1),(H,2,2),(H,2,3),(H,2,4),(H,2,5),(H,2,6),(H,4,1),(H,4,2),(H,4,3),(H,2,4),(H, 4,5),(H,4,6), (H,6,1),(H,6,2),(H,6,3),(H,6,4),(H,6,5),(H,6,6)}

    ➡️Case 3: The outcome is Tail

    ➡️Total number of sample space=1

    ➡️Sample space ST = {(T)}

    ➡️The overall sample spaces

    ➡️S={(H,1),(H,3),(H,5), (H,2,1),(H,2,2),(H,2,3),(H,2,4),(H,2,5),(H,2,6),(H,4,1),(H,4,2),(H,4,3),(H,2,4),(H,4,5),

    S={(H,1),(H,3),(H,5), (H,2,1),(H,2,2),(H,2,3),(H,2,4),(H,2,5),(H,2,6),(H,4,1),(H,4,2),(H,4,3),(H,2,4),(H,4,5),(H,4,6), (H,6,1),(H,6,2),(H,6,3),(H,6,4),(H,6,5),(H,6,6),(T)}

    \Large\mathcal\green{FOLLOW \: ME}

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    0
    2021-08-16T15:58:09+00:00

    Answer:

    A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?

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    \bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }∣

    ANSWER

    ➡️Since either coin can turn up Head (H) or Tail (T), are the possible outcomes.

    ➡️Let us assume that 1, 2, 3, 4, 5 and 6 are the possible outcomes when the die is thrown.

    ➡️The problem can be solved by dividing it into 3 cases

    ➡️Case 1: The outcome is Head and the corresponding number on the die shows Odd number

    ➡️Total number of sample space = (1 × 3) = 3

    Total number of sample space = (1 × 3) = 3Sample space SHO = {(H,1), (H,3), (H,5)}

    ➡️Case 2: The outcome is Head and the corresponding number on the die shows Even number

    ➡️Total number of sample space = (1 × 3 × 6) = 18

    ➡️SHE={(H,2,1),(H,2,2),(H,2,3),(H,2,4),(H,2,5),(H,2,6),(H,4,1),(H,4,2),(H,4,3),(H,2,4),(H, 4,5),(H,4,6), (H,6,1),(H,6,2),(H,6,3),(H,6,4),(H,6,5),(H,6,6)}

    ➡️Case 3: The outcome is Tail

    ➡️Total number of sample space=1

    ➡️Sample space ST = {(T)}

    ➡️The overall sample spaces

    ➡️S={(H,1),(H,3),(H,5), (H,2,1),(H,2,2),(H,2,3),(H,2,4),(H,2,5),(H,2,6),(H,4,1),(H,4,2),(H,4,3),(H,2,4),(H,4,5),

    S={(H,1),(H,3),(H,5), (H,2,1),(H,2,2),(H,2,3),(H,2,4),(H,2,5),(H,2,6),(H,4,1),(H,4,2),(H,4,3),(H,2,4),(H,4,5),(H,4,6), (H,6,1),(H,6,2),(H,6,3),(H,6,4),(H,6,5),(H,6,6),(T)}

    \Large\mathcal\green{FOLLOW \: ME}FOLLOWME

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