Question

Place

Answer 1

Answer:

$P(A\ and\ B) = \frac{3}{7}$

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;

$S = \{India,\ Tokyo,\ Houston,\ Peru,\ New York,\ Tijuana,\ Canada \}$

$n(S) = 7$

The next is to list events A and B

A = City

$A = \{Tokyo,\ Houston,\ New York,\ Tijuana\}$

B = North America

$B = \{Houston,\ New York,\ Tijuana,\ Canada\}$

The next is to list common elements in A and B

$A\ n\ B = \{Houston,\ New York,\ Tijuana\}$

$n(A\ and\ B) = 3$

The probability of A and B is calculated as follows;

$P(A\ and\ B) = \frac{n(A\ and\ B)}{n(S)}$

Substitute $n(A\ and\ B) = 3$ and $n(S) = 7$ in the expression above

$P(A\ and\ B) = \frac{3}{7}$