A pizza delivery company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1664 customers. The data is summarized in the table below.
Gender and Residence of Customers
Males Females
Apartment 206 149
Dorm 295 276
With Parent(s) 55 68
Sorority/Fraternity House 132 204
Other 180 99
What is the probability that a customer is female and lives in a dorm or is female and lives in 'Other'? Express your answer as a fraction or a decimal number rounded to four decimal places.

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JeanaShupp JeanaShupp · Answer 1 · 2020-10-22T03:37:58+02:00

Answer: 0.2254

Step-by-step explanation:

Let E= Event of getting of female lives in a dorm.

F = Event of getting of female lives in a 'Other'.

From the table , n(E) = 276 and n(F) = 99

and n(E∩F) = 0 [E and F are Mutually exclusive]

Now, n(E∪F)= n(E) + n(F) - n(E∩F)

= 276+99-0

= 375

also, n(S) =1664 (Sample size)

Required probability : [tex]P(E\cup F)=\dfrac{n(E\cup F)}{n(S)}[/tex]

[tex]=\dfrac{375}{1664}\approx0.2254[/tex]

Hence, the probability that a customer is female and lives in a dorm or is female and lives in 'Other' = 0.2254