From a survey involving 1,000 university students, a market research company found that 710 students owned laptops, 470 owned cars, and 320 owned cars and laptops. If a university student is selected at random, what is each (empirical) probability?
(A) The student owns either a car or a laptop
(B) The student owns neither a car nor a laptop.

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JeanaShupp JeanaShupp · Answer 1 · 2019-11-25T06:40:22+01:00

Answer: (A) 0.86

(B) 0.14

Step-by-step explanation:

Given : Total university students n(S)= 1,000

Number of students owned laptops n(L)= 710

Number of students owned cars n(C)= 470

Number of students owned laptops and cars n(L∩C)= 320

Then, the number of students owned either a car or a laptop :

n(L∪C)=n(L)+n(C)-n(L∩C)

=710+470-320=860

Probability that the student owns either a car or a laptop :-

[tex]P(L\cup C)=\dfrac{n(L\cup C)}{n(S)}\\\\=\dfrac{860}{1000}=0.86[/tex]

Probability that the student owns neither a car nor a laptop :-

[tex]P(L'\cap C')=P(L\cup C)'\ [\because (A'\cap B)'=(A\cap B)']\\\\=1-P(L\cup C)\ \ \text{(Using Demorgon's law)}\\\\=1-0.86=0.14[/tex]