SOLUTION: A fair coin is tossed three times and the events A, B, and C are defined as follows: A:{ At least one head is observed } B:{ At least two heads are observed } C:{ The number

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Question 913619: A fair coin is tossed three times and the events A, B, and C 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:
(a) P(Ac) =
(b) P(A∩B) =
(c) P(A∪B∪C) =
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
List out the sample space

HHH
HHT
HTH
HTT

THH
THT
TTH
TTT

There are 8 possible outcomes. Notice how 2^3 = 8.

For parts (a), (b) and (c), I will use the sample space to calculate the probabilities.

(a)

P(A^c) = P(no heads) = 1/8
-------------------------------------------------------

(b)

P(A∩B) = P(at least one head AND at least 2 heads) = P(At least 2 heads)

P(A∩B) = P(At least 2 heads)

P(A∩B) = 4/8

P(A∩B) = 1/2

-------------------------------------------------------

(c)

P(A∪B∪C) = P(at least one head OR at least 2 heads OR # heads odd)

P(A∪B∪C) = P(at least one head OR # heads odd)

P(A∪B∪C) = 7/8

Let me know if you need more help or if you need me to explain a step in more detail.
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Thanks,

Jim