Question

Of 800 people surveyed, 420 were male, and 325 had cell phones. Of those with cell phones, 200 were female. What is the probability that a person surveyed was either male or had a cell phone?

Answer 1

The probability that a person surveyed was either male or had a cell phone is 0.775.

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:

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

Compute the probability of selecting a male as follows:

`P (M) = (420)/(800)=0.525`

Compute the probability that a person had a cell phone as follows:

`P(X)=(325)/(800)=0.40625`

Compute the probability that a person is male and had a cell phone as follows:

`P(M\cap X)=(125)/(800)=0.15625`

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)`

`=0.525+0.40625-0.15625\\=0.775`

Thus, the probability that a person surveyed was either male or had a cell phone is 0.775.