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

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.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim
RELATED QUESTIONS
: A fair coin is tossed three times and the events A, B, and C are defined as follows:... (answered by greenestamps)

A coin is tossed three times. What is the probability of getting A. Two heads and a tail... (answered by math_helper)

A fair coin is tossed 4 times what is the probability that exactly one head appears and... (answered by Fombitz)

A fair coin is tossed 2 times, and the events A and B (answered by ikleyn)

A fair coin is tossed 5 successive times . what is the probability that at least one head (answered by stanbon)

A fair coin is tossed 3 times. Find the probability of obtaining at least one head. a (answered by Edwin McCravy)

A coin is tossed 3 times. define the events A and B as: A = {num heads > num tails} B = (answered by ikleyn)

A coin is tossed 3 times. define the events A and B as: A = {num heads > num tails} B = (answered by greenestamps,ikleyn)

A coin is tossed 3 times. define the events A and B as: A = {num heads > num tails} B (answered by ikleyn)