Question

The table below contains the results of 400 employed adults where people were asked if they felt tense or stressed out at work

Gender	Yes	No
Male	89	111
Female	93	107

a. What is the probability that a randomly selected person will be male?

b. Given that the employed person felt tense or stressed out at work, what is the probability that the employed person was female?

c. Given that the employed person is female, what is the probability that she felt tense or stressed out at work?

d. Is feeling tense or stressed out at work independent of gender? Briefly explain.

Answer 1

Total number of employees = 400

Number of male = 89 + 111 = 200

a) The probability that a randomly selected person will be male

$= \frac{200}{400}$

$= 0.5$

b) Number of people who felt tense or stressed out at work = 89 + 93 = 182

Given that the employed person felt tense or stressed out at work, the probability that the employed person was female

$= \frac{93}{182}$

$= 0.511$

c) Number of female = 93 +107 = 200

Given that the employed person is female, the probability that she felt tense or stressed out at work

$= \frac{93}{200}$

$= 0.465$

d) P( feeling tense or stressed out at work | female) = 0.511

and P( feeling tense or stressed out at work) $= \frac{182}{400} = 0.455$

Here,

P( feeling tense or stressed out at work | female) $\neq$ P( feeling tense or stressed out at work)

So, we can write, feeling tense or stressed out at work is not independent of gender.