Question 913619
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

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(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


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(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