Answer:
The probability that a person surveyed was either male or had a cell phone is 0.775.
Step-by-step explanation:
Denote the events as follows:
<em>M</em> = a person is male
<em>F</em> = a person is female
<em>X</em> = a person has a cell phone
<em>Y</em> = a person does not have a cell phone
The information provided is:
N = 800
n (M) = 420
n (X) = 325
n (X ∩ F) = 200
The remaining data is computed as follows:
M F Total
X <u>125</u> 200 325
Y <u>295</u> <u>180</u> <u>475</u>
Total 420 <u>380</u> 800
The probability of the union of two events is given by:
![P(A\cup B)=P(A)+P(B)-P(A\cap B)](https://tex.z-dn.net/?f=P%28A%5Ccup%20B%29%3DP%28A%29%2BP%28B%29-P%28A%5Ccap%20B%29)
Compute the probability of selecting a male as follows:
![P (M) = \frac{420}{800}=0.525](https://tex.z-dn.net/?f=P%20%28M%29%20%3D%20%5Cfrac%7B420%7D%7B800%7D%3D0.525)
Compute the probability that a person had a cell phone as follows:
![P(X)=\frac{325}{800}=0.40625](https://tex.z-dn.net/?f=P%28X%29%3D%5Cfrac%7B325%7D%7B800%7D%3D0.40625)
Compute the probability that a person is male and had a cell phone as follows:
![P(M\cap X)=\frac{125}{800}=0.15625](https://tex.z-dn.net/?f=P%28M%5Ccap%20X%29%3D%5Cfrac%7B125%7D%7B800%7D%3D0.15625)
Compute the probability that a person surveyed was either male or had a cell phone as follows:
![P(M\cup X)=P(M)+P(X)-P(M\cap X)](https://tex.z-dn.net/?f=P%28M%5Ccup%20X%29%3DP%28M%29%2BP%28X%29-P%28M%5Ccap%20X%29)
![=0.525+0.40625-0.15625\\=0.775](https://tex.z-dn.net/?f=%3D0.525%2B0.40625-0.15625%5C%5C%3D0.775)
Thus, the probability that a person surveyed was either male or had a cell phone is 0.775.