Question

A survey of 400 employed adults asked if they felt tense or stressed out at work with the accompanying results. Complete parts? (a) through? (d) below. Felt Tense or Stressed out at Work Females- Yes (108) No (92) Males Yes (99) No (101)

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

b. Given that the employed adult is? female, what is the probability that she felt tense or stressed out at? work? Explain the difference in the results in? (a) and? (b).

The conditional events are reversed.

B.

The numerator and denominator of the probability is reversed.

C.

Part? (a) is a conditional probability while part? (b) is a general probability.

D.

There is no difference in the results in? (a) and? (b). .

Is feeling tense or stressed out at work and gender? independent?

Answer 1

		Tense
		Yes	No	Total
Gender	Female	108	92	200
	Male	99	101	200
	Total	207	193	400

(a)  P(Female | Tense) = P(Female and Tense) / P(Tense) = (108/400) / (207/400) = 108/207 = 0.5217

(b) P(Tense | Female) = P(Tense and Female) / P(Female) = (108/400) / (200/400) = 108/200 = 0.54

(c) The conditional events are reversed.

P(Female | Tense) ≠ P(Female), so gender and feeling tense are not independent.