Question

Intro to probability and statistics.

Please make sure it's readable. And easy to understand. Thanks in advance.

8. Toss a fair coin three times and observe the results.

(a) Specify the sample space.

(b) LetA= “at most one heads”, B = “at least one heads”, andC= “heads on thesecond toss”. FindP(A),P( ̄B),P(A∩B), andP(A∪C).

Answer 1

(a) When a fair coin is tossed 3 times

sample space, S = { HHH HHT HTH HTT

THH THT TTH TTT }

(b) A= at most one heads = { HTT, THT, TTH, TTT}

B= at least on e heads= { HHH, HHT, HTH , HTT, THH, THT, TTH }

C =heads on thesecond toss = { HHH, HHT, THH, THT}

P(at most one heads) = P( A) = P( { HTT, THT, TTH, TTT})

= 4/8

= 1/2 = 0.5

P(at least one heads ) = P( B) = P( { HHH, HHT, HTH , HTT, THH, THT, TTH })

= 7/8

= 0.875

  P(A∩B) = P( { HTT, THT, TTH})

= 3/8

= 0.375

P( AUC) = P( { HTT, THT, TTH, TTT , HHH, HHT, THH }

= 7/8

= 0.875