Question

According to a government statistics? department, 20.6?% of women in a country aged 25 years or older have a? Bachelor's Degree; 16.6?% of women in the country aged 25 years or older have never? married; among women in the country aged 25 years or older who have never? married, 22.2?% have a? Bachelor's Degree; and among women in the country aged 25 years or older who have a? Bachelor's Degree, 17.9?% have never married. Complete parts? (a) and? (b) below. ?(a) Are the events? "have a? Bachelor's Degree" and? "never married"? independent? Explain. The probability of the event? "have a? Bachelor's Degree" is affected by the occurrence of the event? "never married", and the probability of the event? "never married" is affected by the occurrence of the event? "have a? Bachelor's Degree", so the events are not independent. ?(b) Suppose a woman in the country aged 25 years or older is randomly selected. What is the probability she has a? Bachelor's Degree and has never? married? Interpret this probability. The probability is 0.037. ?(Round to three decimal places as? needed.) This probability means that if 100 women in the country aged 25 years or older were randomly? selected, one could expect about 4 of them to have a Bachelor's Degree and never have married.

Answer 1

Here, we are given that:

P( bachelor degree ) = 0.206

P( never married ) = 0.166

P( bachelor's degree | never married ) = 0.222

P( never married | bachelor's degree ) = 0.179

a) Using bayes theorem, we get here:

P( bachelor's degree and never married ) = P( bachelor's degree | never married )P( never married )

P( bachelor's degree and never married ) =  0.222*0.166 = 0.036852

Also P( bachelor degree )P( never married ) = 0.206*0.166 = 0.034196 which is not equal to P( bachelor's degree and never married )

Therefore the two events are not independent.

b) This we already computed above as:

P( bachelor's degree and never married ) = P( bachelor's degree | never married )P( never married )

P( bachelor's degree and never married ) =  0.222*0.166 = 0.036852

Therefore 0.037 is the required probability here.