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Chapter 13: Q 13. (page 847)

If $n (A \cap B) = 10, n (B) = 20, n (A \cup B) = 50$ , find $n (A)$ .

Short Answer

Expert verified

$n (A) = 40$ .

Step by step solution

01

Step 1. Given Information.

The given values are $n (A \cap B) = 10, n (B) = 20, n (A \cup B) = 50$ .

02

Step 2. Calculation of nA.

Using the Counting principle, we get

$\begin{array}{rcl} n (A \cup B) & = & n (A) + n (B) - n (A \cap B) \\ 50 & = & n (A) + 20 - 10 \\ 50 & = & n (A) + 10 \\ n (A) & = & 40 \end{array}$ .

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Most popular questions from this chapter

A golf ball is selected at random from a container. If the container has 9 white balls, 8 green balls, and 3 orange balls, find the probability of each event.

The golf ball is white or orange.

Determine whether the following is a probability model.

Find the value of each permutation.

$P (4, 4)$

Through observation, it has been determined that the probability for a given number of people waiting in line at the “5 items or less” checkout register of a supermarket is as follows:

Find the probability of:

(a) At most 2 people in line

(b) At least 2 people in line

(c) At least 1 person in line

Find the value of each permutation.

$P (8, 4)$

See all solutions

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