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Type of person   Male (M)   Female (F) Employed (E)  5,877,000 4,930,000 Unemployed (U)  349,000 257,000 Not in the labour force (NLF)  2,416,000 3,705,000  According to labour market statistics published by the Australian Bureau of Statistics (ABS), the above data about the employment status of Australian men and women in March 2009 were obtained. Round your answers to two decimal places.a) What is the probability that a person is not in the labour force? P(NLF)b) What is the probability that a female is unemployed? P(F and U)c) If a male person in Australia is selected at random, what is the probability that he will be unemployed? P(U | M)When you have given this question some thought, click on the Answer button to check if you were thinking along the correct lines.

Question

Type of person   Male (M)   Female (F) Employed (E)  5,877,000 4,930,000 Unemployed (U)  349,000 257,000 Not in the labour force (NLF)  2,416,000 3,705,000  According to labour market statistics published by the Australian Bureau of Statistics (ABS), the above data about the employment status of Australian men and women in March 2009 were obtained. Round your answers to two decimal places.a) What is the probability that a person is not in the labour force? P(NLF)b) What is the probability that a female is unemployed? P(F and U)c) If a male person in Australia is selected at random, what is the probability that he will be unemployed? P(U | M)When you have given this question some thought, click on the Answer button to check if you were thinking along the correct lines.

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Solution

a) To find the probability that a person is not in the labour force (P(NLF)), you need to divide the total number of people not in the labour force by the total number of people.

Total number of people = M + F = 5,877,000 (males) + 4,930,000 (females) + 349,000 (unemployed males) + 257,000 (unemployed females) + 2,416,000 (males not in labour force) + 3,705,000 (females not in labour force) = 17,534,000

Total number of people not in the labour force = NLF = 2,416,000 (males) + 3,705,000 (females) = 6,121,000

So, P(NLF) = NLF / Total number of people = 6,121,000 / 17,534,000 = 0.349 or 34.9%

b) To find the probability that a female is unemployed (P(F and U)), you need to divide the number of unemployed females by the total number of people.

Number of unemployed females = 257,000

So, P(F and U) = Number of unemployed females / Total number of people = 257,000 / 17,534,000 = 0.0147 or 1.47%

c) To find the probability that a male will be unemployed if a male person in Australia is selected at random (P(U | M)), you need to divide the number of unemployed males by the total number of males.

Total number of males = M = 5,877,000 (employed) + 349,000 (unemployed) + 2,416,000 (not in labour force) = 8,642,000

Number of unemployed males = 349,000

So, P(U | M) = Number of unemployed males / Total number of males = 349,000 / 8,642,000 = 0.0404 or 4.04%

This problem has been solved

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