A survey was conducted to obtain information on alcohol consumption. A random sample of males gave: Marital Status teetotal drinking 1-20 units/week drinking 21+units/week Totalsingle 83 283 98 464married 427 608 150 1185divorced 92 50 9 151widowed 31 51 18 100Totals 633 992 275 1900 Find the following probabilities that a randomly chosen male involved in this survey (i) is single       (Give your answer correct to 3 decimal places )    (ii) is drinking 1-20 units/week   (Give your answer correct to 3 decimal places )     (iii) is either single or married  (Give your answer correct to 3 decimal places )         (iv) is teetotal or drinking 21+ units/week   (Give your answer correct to 3 decimal places )   (v) is widowed and teetotal

(i) The probability that a randomly chosen male is single can be calculated by dividing the total number of single males by the total number of males in the survey.

So, P(single) = Number of single males / Total number of males = 464 / 1900 = 0.244.

(ii) The probability that a randomly chosen male is drinking 1-20 units/week can be calculated by dividing the total number of males drinking 1-20 units/week by the total number of males in the survey.

So, P(drinking 1-20 units/week) = Number of males drinking 1-20 units/week / Total number of males = 992 / 1900 = 0.522.

(iii) The probability that a randomly chosen male is either single or married can be calculated by adding the number of single males and the number of married males, and then dividing by the total number of males in the survey.

So, P(single or married) = (Number of single males + Number of married males) / Total number of males = (464 + 1185) / 1900 = 0.868.

(iv) The probability that a randomly chosen male is either teetotal or drinking 21+ units/week can be calculated by adding the number of teetotal males and the number of males drinking 21+ units/week, and then dividing by the total number of males in the survey.

So, P(teetotal or drinking 21+ units/week) = (Number of teetotal males + Number of males drinking 21+ units/week) / Total number of males = (633 + 275) / 1900 = 0.477.

(v) The probability that a randomly chosen male is widowed and teetotal can be calculated by dividing the number of widowed and teetotal males by the total number of males in the survey.

So, P(widowed and teetotal) = Number of widowed and teetotal males / Total number of males = 31 / 1900 = 0.016.

All probabilities are rounded to three decimal places.