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}.
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](https://tex.z-dn.net/?f=%5Ctext%7BP%28Exactly%20one%20tail%29%7D%20%3D%20%5Cdfrac%7B3%7D%7B8%7D%20%3D%200.375)
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](https://tex.z-dn.net/?f=%5Ctext%7BP%28Exactly%20two%20tail%29%7D%20%3D%20%5Cdfrac%7B3%7D%7B8%7D%20%3D%200.375)
3. The probability of getting a head on the first toss
P(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](https://tex.z-dn.net/?f=%5Ctext%7BP%28head%20on%20the%20first%20toss%29%7D%20%3D%20%5Cdfrac%7B4%7D%7B8%7D%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%3D%200.5)
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](https://tex.z-dn.net/?f=%5Ctext%7BP%28tail%20on%20the%20last%20toss%29%7D%20%3D%20%5Cdfrac%7B4%7D%7B8%7D%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%3D%200.5)
5. The probability of getting at least one head
P(at least one head)
Favorable outcomes ={HHH, HHT, HTH, HTT, THH, THT, TTH}
![\text{P(at least one head)} = \dfrac{7}{8} = 0.875](https://tex.z-dn.net/?f=%5Ctext%7BP%28at%20least%20one%20head%29%7D%20%3D%20%5Cdfrac%7B7%7D%7B8%7D%20%3D%200.875)
6. The probability of getting at least two heads
P(Exactly one tail)
Favorable outcomes ={HHH, HHT, HTH,THH}
![\text{P(Exactly one tail)} = \dfrac{4}{8} = \dfrac{1}{2} = 0.5](https://tex.z-dn.net/?f=%5Ctext%7BP%28Exactly%20one%20tail%29%7D%20%3D%20%5Cdfrac%7B4%7D%7B8%7D%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%3D%200.5)