Question

A survey was given with 125 respondents about raising minimum wage. Results are shown in a two way table below.

	for raising	against raising	no opinion	total
age 21-40	35	20	5	60
age 41-50	30	35	20	85
total	45	55	35	145

i) What is the probavility the respondent is of age 21-40, and has no opion?

ii) Given that a respondent is of age 21-40, what is the probability the respondent is against raising the minimum wage?

iv) Are the events 'For raising minimum wage' and 'aged 21-40' independent? Support your answer with a calculation

Answer 1

i)

Probability the respondent is of age 21-40, and has no opinion = Number of respondent of age 21-40, and has no opinion / Grand Total

= 5 / 145

= 0.03448276

ii)

Given that a respondent is of age 21-40, the probability the respondent is against raising the minimum wage

= Number of the respondent of age 21-40 and against raising the minimum wage / Number of the respondent of age 21-40

= 20 / 60

= 0.3333333

iii)

P(For raising minimum wage and 'aged 21-40' independent) = Number of the respondent of age 21-40 and for raising the minimum wage / Grand Total = 35 / 145 = 0.2413793

P(For raising minimum wage) = Number of the respondent for raising the minimum wage / Grand Total

= 45 / 145 = 0.3103448

P(aged 21-40' independent) = Number of the respondent of age 21-40 / Grand Total

= 60 / 145 = 0.4137931

P(For raising minimum wage) * P(aged 21-40' independent) = 0.3103448 * 0.4137931 = 0.1284185

Since, P(For raising minimum wage and 'aged 21-40' independent) P(For raising minimum wage) * P(aged 21-40' independent)

the events 'For raising minimum wage' and 'aged 21-40' are not independent.