Question

A perfectly balanced coin is tossed, there is equal chance to get a head (H) or a tail (T ). Consider a random experiment of throwing SEVEN perfectly balanced and identical coins. Let S denote the sample space.

a) List the elements in S.

(b) Find the probability that there is three tails and four heads.

Answer 1

a. S={HHHHHHH,HHHHHHT,HHHHHTH,HHHHHTT,HHHHTHH,HHHHTHT,HHHHTTH,HHHHTTT, HHHTHHH,HHHTHHT,HHHTHTH,HHHTHTT,HHHTTHH,HHHTTHT,HHHTTTH,HHHTTTT,HHTHHHH,HHTHHHT, HHTHHTH,HHTHHTT,HHTHTHH,HHTHTHT,HHTHTTH,HHTHTTT,HHTTHHH,HHTTHHT,HHTTHTH,HHTTHTT, HHTTTHH,HHTTTHT,HHTTTTH,HHTTTTT,HTHHHHH,HTHHHHT,HTHHHTH,HTHHHTT,HTHHTHH,HTHHTHT, HTHHTTH,HTHHTTT,HTHTHHH,HTHTHHT,HTHTHTH,HTHTHTT,HTHTTHH,HTHTTHT,HTHTTTH,HTHTTTT, HTTHHHH,HTTHHHT,HTTHHTH,HTTHHTT,HTTHTHH,HTTHTHT,HTTHTTH,HTTHTTT,HTTTHHH,HTTTHHT, HTTTHTH,HTTTHTT,HTTTTHH,HTTTTHT,HTTTTTH,HTTTTTT,THHHHHH,THHHHHT,THHHHTH,THHHHTT, THHHTHH,THHHTHT,THHHTTH,THHHTTT,THHTHHH,THHTHHT,THHTHTH,THHTHTT,THHTTHH,THHTTHT, THHTTTH,THHTTTT,THTHHHH,THTHHHT,THTHHTH,THTHHTT,THTHTHH,THTHTHT,THTHTTH,THTHTTT, THTTHHH,THTTHHT,THTTHTH,THTTHTT,THTTTHH,THTTTHT,THTTTTH,THTTTTT,TTHHHHH,TTHHHHT, TTHHHTH,TTHHHTT,TTHHTHH,TTHHTHT,TTHHTTH,TTHHTTT,TTHTHHH,TTHTHHT,TTHTHTH,TTHTHTT, TTHTTHH,TTHTTHT,TTHTTTH,TTHTTTT,TTTHHHH,TTTHHHT,TTTHHTH,TTTHHTT,TTTHTHH,TTTHTHT, TTTHTTH,TTTHTTT,TTTTHHH,TTTTHHT,TTTTHTH,TTTTHTT,TTTTTHH,TTTTTHT,TTTTTTH,TTTTTTT}