Among DGc + 150 = _____ employees of a Tattoo Company, a total of 130 have tatto
ID: 3224174 • Letter: A
Question
Among DGc + 150 = _____ employees of a Tattoo Company, a total of 130 have tattoos. There are 150 males working for this company and 85 of the males have tattoos. (I) What is the probability that an employee selected at random: (a) Is a female? (b) has a tattoo? (c) Is a female and has a tattoo? (d) Is a male and does not have tattoo? (e) Is male or has a tattoo? (f) Is a female or does not has a tattoo? (a) Assume we selected a female of the company, what is the probability she has no tattoo? (b) Assume we selected a male from the company, what is the probability he has a tattoo? (c) Are having a tattoo and the gender of the employee independent? Explain.Explanation / Answer
Total employees = 471
Total male employees = 150
Therefore total female employees = 321
Also number of males with tattoo = 85
As total 130 have tattoo, therefore number of females with tattoo would be = 130 - 85 = 45
(II) a) Given a female is selected, probability that she has no tattoo would be:
= P ( no tattoo | Female )
= number of females with no tattoo / number of females
= ( 321 - 45 ) / 321 = 0.8598
Therefore 0.8598 is the required probability.
b) Given a male is selected, probability he has a tattoo:
= number of males with tattoo / number of males
= 85 / 150 = 0.5667
Therefore 0.5667 is the required probability.
c) To compute that having a tattoo and the gender of the employee, we can compute:
P( tattoo ) = 130 / 471 = 0.276
P ( female ) = 321 / 471 = 0.6815
P( tattoo, female ) = 45 / 471 = 0.0955
Now we see that:
P ( tattoo ) P( female ) = 0.276*0.6815 = 0.188094 which is not equal to 0.0955. Therefore the 2 events are not independent of each other.
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