Find the probability for the experiment of tossing a coin three times. Use the sample space S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.

Question

Find the probability for the experiment of tossing a coin three times. Use the sample space S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
1. The probability of getting exactly one tail
2. The probability of getting exactly two tails
3. The probability of getting a head on the first toss
4. The probability of getting a tail on the last toss
5. The probability of getting at least one head
6. The probability of getting at least two heads

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Delilah 3 months 2022-02-09T06:06:49+00:00 1 Answer 0 views 0

Answers ( )

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    2022-02-09T06:08:43+00:00

    Answer:

    1) 0.375

    2) 0.375

    3) 0.5

    4) 0.5

    5) 0.875

    6) 0.5                          

    Step-by-step explanation:

    We are given the following in the question:

    Sample space, S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.

    [tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]

    1. The probability of getting exactly one tail

    P(Exactly one tail)

    Favorable outcomes ={HHT, HTH, THH}

    [tex]\text{P(Exactly one tail)} = \dfrac{3}{8} = 0.375[/tex]

    2. The probability of getting exactly two tails

    P(Exactly two tail)

    Favorable outcomes ={ HTT,THT, TTH}

    [tex]\text{P(Exactly two tail)} = \dfrac{3}{8} = 0.375[/tex]

    3. The probability of getting a head on the first toss

    P(head on the first toss)

    Favorable outcomes ={HHH, HHT, HTH, HTT}

    [tex]\text{P(head on the first toss)} = \dfrac{4}{8} = \dfrac{1}{2} = 0.5[/tex]

    4. The probability of getting a tail on the last toss

    P(tail on the last toss)

    Favorable outcomes ={HHT,HTT,THT,TTT}

    [tex]\text{P(tail on the last toss)} = \dfrac{4}{8} = \dfrac{1}{2} = 0.5[/tex]

    5. The probability of getting at least one head

    P(at least one head)

    Favorable outcomes ={HHH, HHT, HTH, HTT, THH, THT, TTH}

    [tex]\text{P(at least one head)} = \dfrac{7}{8} = 0.875[/tex]

    6. The probability of getting at least two heads

    P(Exactly one tail)

    Favorable outcomes ={HHH, HHT, HTH,THH}

    [tex]\text{P(Exactly one tail)} = \dfrac{4}{8} = \dfrac{1}{2} = 0.5[/tex]

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