SOLUTION: six cions are flipped simultaneously. What is the probability that there are: A) At least 5 heads? B) At least 3 tails? C) No heads? D) at most 2 tails?

Question 1014641: six cions are flipped simultaneously. What is the probability that there are:
A) At least 5 heads?
B) At least 3 tails?
C) No heads?
D) at most 2 tails?
Answer by skippo(9) (Show Source): You can put this solution on YOUR website!
six cions are flipped simultaneously. What is the probability that there are:
A) At least 5 heads?
B) At least 3 tails?
C) No heads?
D) at most 2 tails?
solution
The sample space S= [HHHHHH, HHHHHT, HHHHTH, HHHHTT, HHHTHH, HHHTHT, HHHTTH, HHHTTT, HHTHHH, HHTHHT, HHTHTH, HHTHTT, HHTTHH, HHTTHT, HHTTTH, HHTTTT, HTHHHH, HTHHHT, HTHHTH, HTHHTT, HTHTHH, HTHTHT, HTHTTH, HTHTTT, HTTHHH, HTTHHT, HTTHTH, HTTHTT, HTTTHH, HTTTHT, HTTTTH, HTTTTT, THHHHH, THHHHT, THHHTH, THHHTT, THHTHH, THHTHT, THHTTH, THHTTT, THTHHH, THTHHT, THTHTH, THTHTT, THTTHH, THTTHT, THTTTH, THTTTT, TTHHHH, TTHHHT, TTHHTH, TTHHTT, TTHTHH, TTHTHT, TTHTTH, TTHTTT, TTTHHH, TTTHHT, TTTHTH, TTTHTT, TTTTHH, TTTTHT, TTTTTH, TTTTTT]

a) P(at least 5 heads) = P(5 heads or more)= 7/64
b) P(at least 3 tails) = P(3 tails or more)= 42/64
c) P(no heads) = 1/64
d) P(at most 2 tails) = P(2 tails or less) = 22/64
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