(a) {HEAD,TAIL}
(b) {1,2,3,4,5,6}
(c)
{(HEAD,1),(HEAD,2),(HEAD,3),(HEAD,4),(HEAD,5),(HEAD,6),(TAIL,1),(TAIL,2),(TAIL,3),(TAIL,4),(TAIL,5),(TAIL,6)}
The sample space of combination of the experiments has 12 elements with equal probabilities 121.
A∩B={(HEAD,1),(HEAD,3),(HEAD,5)},
∣A∩B∣=3, hence P(A∩B)=3⋅121=41.
A∪B={(HEAD,1),(HEAD,2),(HEAD,3),(HEAD,4),(HEAD,5),(HEAD,6),(TAIL,1),(TAIL,3),(TAIL,5)},
∣A∪B∣=9, hence P(A∪B)=9⋅121=43.
Answer: P(A∩B)=41,P(A∪B)=3⋅121=43.
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