Answer to Question #347021 in Statistics and Probability for Muhammad Zohaib

Question #347021

two good dice are rolled simultaneously. let a denote the event “ the sum shown is 8" and b the event “the two show the same number". find p(a), p(b), p(a ∩ b), and p(a ∪ b).

1
Expert's answer
2022-06-02T12:40:51-0400
123456123456723456783456789456789105678910116789101112\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c:c} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 2 & 3 & 4 & 5 & 6 & 7\\ \hdashline 2 & 3 & 4 & 5 & 6 & 7 & 8\\ \hdashline 3 & 4 & 5 & 6 & 7 & 8 & 9\\ \hdashline 4 & 5 & 6 & 7 & 8 & 9 & 10\\ \hdashline 5 & 6 & 7 & 8 & 9 & 10 & 11\\ \hdashline 6 & 7 & 8 & 9 & 10 & 11 & 12\\ \hdashline \end{array}

The sum shown is 8: 2+6=3+5=4+4=5+3=6+2

The same number: (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)(1,1), (2,2), (3,3), (4,4), (5,5),(6,6)


a)

P(A)=536P(A)=\dfrac{5}{36}

b)

P(B)=636=16P(B)=\dfrac{6}{36}=\dfrac{1}{6}

c)


PAB)=136PA\cap B)=\dfrac{1}{36}

d)


PAB)=1036=518PA\cup B)=\dfrac{10}{36}=\dfrac{5}{18}


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