Math Help - Mutually/ NonMutually Exclusive events

1. Mutually/ NonMutually Exclusive events

I'm still confuse about these events. Also 180 + 160 is more than 300. Where have I made the mistake?

The owners of a music store placed ads in the newspaper and on TV advertising their annual 40% sale. They did a survey of the first 300 customers, and discovered that 180 saw the ad on tv, 160 saw the ad in the newspaper and 75 saw the on TV and in the newspaper. What is the probability that a randomly select customer

75/100
P(AandB) = P(A) + P(B) = 160/300 + 180/300 - (it is not a probability!!)
c. did not see the ad?
P(AorB) = P(A) + P(B) - P(AandB)= 160/300 + 180/300-??

2. You seem to have messed up everything here.. First of all, your questions tells you that 300 people were interviewed. Then what made you write that the people saw the advertisement in the newspaper and on Tv is 75/100???

also you seem to be unclear about union, intersection, and complement of sets..

(a) find $P(A \cap B)$ the denominator you have written for (a) is wrong!!

(b) find $P(A \cup B)$

(c) Do you know what complement of a set means? See the defintion in your book/notes

3. Hello, terminator!

The owners of a music store placed ads in the newspaper and on TV

They did a survey of the first 300 customers and discovered that:
180 saw the ad on TV,
160 saw the ad in the paper,
75 saw the on TV and in the paper.

$\begin{array}{ccc}P(\text{TV}) &=& \dfrac{180}{300} \\ \\[-2mm]
P(\text{news}) &=& \dfrac{160}{300} \\ \\[-3mm]
P(\text{TV} \wedge \text{news}) &=& \dfrac{75}{300} \end{array}$

What is the probability that a randomly selected customer

$P(\text{TV} \wedge\text{paper}) \;=\;\dfrac{75}{300} \;=\;\dfrac{1}{4}$

$P(\text{TV} \vee\text{paper}) \;=\;P(\text{TV}) + P(\text{paper}) - P(\text{TV} \wedge\text{paper})$

. . . . . . . . . . . . $=\;\dfrac{180}{300} + \dfrac{160}{300} - \dfrac{75}{300} \;=\;\dfrac{265}{300} \;=\;\dfrac{53}{60}$

c. did not see the ad?

This is the opposite of part (b).

$P(\text{not TV} \wedge \text{not paper}) \;=\;1 - \dfrac{53}{60} \;=\;\dfrac{7}{60}$