Respuesta :
If we were to put this in terms of a venn diagram, we would have 360 owning only brand X, 500 owning only brand Y, and 80 in between, owning both. Therefore, 80 out of the 580 owners of brand Y may have X as well, which we put into fraction form 80/580, and reduce to 4/29.
Answer: The probability that a student chosen at random has a brand X mobile phone given that he has a brand Y mobile phone is 4/29.
Step-by-step explanation:
Since, the total number of students, n(s) = 1,000
The number of students who have X mobile phones, n(X) = 420,
And, number of students who have Y mobile phones, n(Y) = 580,
Thus, the probability of the student that has Y phones,
[tex]P(Y)=\frac{n(Y)}{n(S)}=\frac{580}{1000}=0.58[/tex]
While, the number of students who have both phones, n(X∩Y) = 80
Thus, the probability of the student who has both phones,
[tex]P(X\cap Y)=\frac{n(X\cap Y)}{n(S)}=\frac{80}{1000}=0.08[/tex]
Hence, the probability that a student chosen at random has a brand X mobile phone given that he has a brand Y mobile phone.
[tex]P(\frac{X}{Y})=\frac{P(X\cap Y)}{P(Y)}[/tex]
[tex]=\frac{0.08}{0.58}[/tex]
[tex]=\frac{8}{58}=\frac{4}{29}[/tex]
Hence, the required probability is 4/29.
