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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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2022-02-09T06:06:49+00:00
2022-02-09T06:06:49+00:00 1 Answer
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## Answers ( )

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 followingin 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 tailP(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 tailsP(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 tossP(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 tossP(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 headP(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 headsP(Exactly one tail)

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

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