Answer:
Explained below.
Step-by-step explanation:
The sample space for flipping a dollar twice is:
S = {HH, HT, TH, TT}
n (S) = 4
Independent events are those events that does not affect each other.
In this case, the outcomes of the two tosses are independent, i.e. the outcome of the second toss does not depends on the second toss.
(1)
Compute the probability of a head on the first flip:
The favorable outcomes are:
H₁ = {HH, HT}
n (H₁) = 2
(2)
Compute the probability of a tail on the second flip given that the first toss was a head:
The favorable outcomes are:
T₂ | H₁ = {HT}
n (T₂ | H₁) = 1
(3)
Compute the probability of two tails:
T₁ and T₂ = {TT}
n (T₁ and T₂) = 1
(4)
Compute the probability of a tail on the first and a head on the second:
T₁ and H₂ = {TH}
n (T₁ and H₂) = 1
(5)
Compute the probability of at least one head on the two flips:
s = {HH, HT, TH}
n (s) = 3