Answer:
[tex]P(A\ and\ B) = \frac{3}{7}[/tex]
Step-by-step explanation:
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Required
Find P(A n B)
where
A = Event that the place is a city
B = Event that the place is in North
The first step is to get the sample space;
Let S represent the sample space;
[tex]S = \{India,\ Tokyo,\ Houston,\ Peru,\ New York,\ Tijuana,\ Canada \}[/tex]
[tex]n(S) = 7[/tex]
The next is to list events A and B
A = City
[tex]A = \{Tokyo,\ Houston,\ New York,\ Tijuana\}[/tex]
B = North America
[tex]B = \{Houston,\ New York,\ Tijuana,\ Canada\}[/tex]
The next is to list common elements in A and B
[tex]A\ n\ B = \{Houston,\ New York,\ Tijuana\}[/tex]
[tex]n(A\ and\ B) = 3[/tex]
The probability of A and B is calculated as follows;
[tex]P(A\ and\ B) = \frac{n(A\ and\ B)}{n(S)}[/tex]
Substitute [tex]n(A\ and\ B) = 3[/tex] and [tex]n(S) = 7[/tex] in the expression above
[tex]P(A\ and\ B) = \frac{3}{7}[/tex]
