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

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}.

$$\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$$

1. The probability of getting exactly one tail

P(Exactly one tail)

Favorable outcomes ={HHT, HTH, THH}

$$\text{P(Exactly one tail)} = \dfrac{3}{8} = 0.375$$

2. The probability of getting exactly two tails

P(Exactly two tail)

Favorable outcomes ={ HTT,THT, TTH}

$$\text{P(Exactly two tail)} = \dfrac{3}{8} = 0.375$$

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

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

$$\text{P(head on the first toss)} = \dfrac{4}{8} = \dfrac{1}{2} = 0.5$$

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

P(tail on the last toss)

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

$$\text{P(tail on the last toss)} = \dfrac{4}{8} = \dfrac{1}{2} = 0.5$$

5. The probability of getting at least one head

$$\text{P(at least one head)} = \dfrac{7}{8} = 0.875$$
$$\text{P(Exactly one tail)} = \dfrac{4}{8} = \dfrac{1}{2} = 0.5$$