Question

Suppose two balanced coins are tossed and theupper faces are observed.(a) List the sample points for this experiment.(b) Assign a reasonable probability to each sample point. (Are the samplepoints equally likely?) [HINT: Write down your ‘Belief’.](c) LetAdenote the event that exactly one head is observed andBthe eventthat at least one head is observed. List the sample points inAandBseparately.(d) From your answer to part (c), find Pr(A), Pr(B), Pr(A∩B), Pr(A∪B)and Pr(Ac∪B).

Answer 1

Explanation:

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