Answer :
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:
M = a person is male
F = a person is female
X = a person has a cell phone
Y = 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 125 200 325
Y 295 180 475
Total 420 380 800
The probability of the union of two events is given by:
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]
Compute the probability of selecting a male as follows:
[tex]P (M) = \frac{420}{800}=0.525[/tex]
Compute the probability that a person had a cell phone as follows:
[tex]P(X)=\frac{325}{800}=0.40625[/tex]
Compute the probability that a person is male and had a cell phone as follows:
[tex]P(M\cap X)=\frac{125}{800}=0.15625[/tex]
Compute the probability that a person surveyed was either male or had a cell phone as follows:
[tex]P(M\cup X)=P(M)+P(X)-P(M\cap X)[/tex]
[tex]=0.525+0.40625-0.15625\\=0.775[/tex]
Thus, the probability that a person surveyed was either male or had a cell phone is 0.775.