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suppose two balanced coins are tossed and the upper faces are observed. a list the sample points for this experiment. b assign a reasonable probability to each sample point. (are the sample points equally likely?) c let a denote the event that exactly one head is observed and b the event that at least one head is observed. list the sample points in both a and b. d from your answer to part (c), find p(a), p(b), p(a ∩ b), p(a ∪ b), and p(a ∪ b). wackerly, dennis; mendenhall, william; scheaffer, richard l.. mathematical statistics with applications (p. 34). cengage textbook. kindle edition.

Sagot :

The probabilities are P(A)= 1/2 , P(B)= 3/4, P(A∩B)= 1/2 , P(AUB)=3/4

given that two balanced coin are tossed and upper faces are observed the samples point of this experiment are

A) 1){H, H}

   2){H, T}

   3){T, H}

  4){T, T}

B) The coin is balanced, so the probability is the same for Tail or head, the first throw is independent of the second. then I can multiply their probabilities:

P(H1∩H2)=P(H)*P(H)=1/2*1/2=1/4

P(H1∩T2)=P(H)*P(H)=1/2*1/2=1/4

P(T1∩H2)=P(H)*P(H)=1/2*1/2=1/4

P(T1∩T2)=P(H)*P(H)=1/2*1/2=1/4

C) A={{T, H}, {H, T}}, B={{H, H}, {H, T}, {T, H}}

D) P(A)=P(H1∩T2)+P(T1∩H2)=1/4+1/4=1/2

P(B)=P(H1∩H2)+P(H1∩T2)+P(T1∩H2)=1/4+1/4+1/4=3/4

P(A∩B)=P(H1∩T2)+P(T1∩H2)=P(A)=1/2

P(AUB)=P(H1∩H2)+P(H1∩T2)+P(T1∩H2)=P(B)=3/4

Ac={{T, T}, {H, H}}

P(AcUB)=P(H1∩H2)=1/4

learn more about of probability here

https://brainly.com/question/13286329

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