SOLUTION: A silver dollar is flipped twice. Calculate the proability of each of the following occurring: a) a head on the first flip b) a tail on the second flip given that the first toss

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Question 316832: A silver dollar is flipped twice. Calculate the proability of each of the following occurring:
a) a head on the first flip
b) a tail on the second flip given that the first toss was a head
c) two tails
d) a tail on the first and a head on the second
e) a tail on the first and a head on the second or a head on the first and a tail on the second
e) at least one head on the two flips
Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A silver dollar is flipped twice. Calculate the proability of each of the following occurring:
Note: The flip results are independent and P(H)=P(T)=1/2
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a) a head on the first flip:: 1/2
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b) a tail on the second flip given that the first toss was a head::1/2
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c) two tails:::(1/2)(1/2) = 1/4
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d) a tail on the first and a head on the second: (1/2)(1/2)= 1/4
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e) a tail on the first and a head on the second or a head on the first and a tail on the second:::(1/2)(1/2) + (1/2)(1/2) = 2/4 = 1/2
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e) at least one head on the two flips::: 1 - P(no heads) = 1-(1/4) = 3/4
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Cheers,
Stan H.
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Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a) Look at the 2 possible outcomes.
H
T
P(H)=1/2
.
.
b) Look at the 2 possible outcomes.
H H
H T
P(T)=1/2
.
.
c)Look at the 4 possible outcomes.
H H
H T
T H
T T
P(T,T)=1/4
.
.
d)Look at the 4 possible outcomes.
H H
H T
T H
T T
P(T,H)=1/4
.
.
e) From d) P(T,H)=1/4
P(H,T)=1/4
P(T,H or H,T)=1/4+1/4=1/2
.
.
f)
P(at least one head)+P(all tails)=1
P(at least one head)=1-P(T,T)
P(at least one head)=1-1/4
P(at least one head)=3/4