FINITE

R

RMS

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Oct 29, 2005
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A fair coin is tossed three times and the events A,B ,C and are defined as follows:

A: At least one head is observed
B: At least two heads are observed
C:The number of heads observed is odd

Find the following probabilities by summing the probabilities of the appropriate sample points:

P (C)= 3/6

HOW ABOUT THESE

P (A U C) =


P (Ac U Bc U C)=


THANKS IN ADVANCE
 
Instead of saying [A U C] say A or C that makes it easier to understand

Second would be write the sample space:

HHH
HTT
THT
TTH
HHT
HTH
THH
TTT

for a total of 8

P[A] includes P[1head, 2heads, 3heads] = 7/8
P includes P[2heads, 3heads] = 4/8
P[C] includes P[1head, 3heads] = 4/8

P[A U C] means P[A or C] = 7/8
this is same as P[A] as C is subset of A

P[Ac U Bc U C]
= P[no heads or less than two heads or one head or three heads]
= 8/8 = 1

We could have solved the sums by the formula
P[A U B] = P[A] +P +P[A int B]

but considering the small sample size it is easier to solve the sums by listing the sample space.
 
I don't understand part c- the answer came out incorrect on my homework site. It says at least two heads but do I need to add a,b, and c together? The way that I am adding them is not coming out correctly?
thank you
 
Oooops my mistake here, in the sum we have all events excet two heads, so that makes the probability 5/8
 
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