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

Question

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).

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c:c:c} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 2 & 3 & 4 & 5 & 6 & 7\\ \hdashline 2 & 3 & 4 & 5 & 6 & 7 & 8\\ \hdashline 3 & 4 & 5 & 6 & 7 & 8 & 9\\ \hdashline 4 & 5 & 6 & 7 & 8 & 9 & 10\\ \hdashline 5 & 6 & 7 & 8 & 9 & 10 & 11\\ \hdashline 6 & 7 & 8 & 9 & 10 & 11 & 12\\ \hdashline \end{array}$$

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

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

a)

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

b)

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

c)

$$PA\cap B)=\dfrac{1}{36}$$

d)

$$PA\cup B)=\dfrac{10}{36}=\dfrac{5}{18}$$