according to the us bureaof labor statistics, 75% of women 25-49 years of age pa
ID: 3334170 • Letter: A
Question
according to the us bureaof labor statistics, 75% of women 25-49 years of age participate in the labor force, 78% of women in that age group are married and 61% are married and participate in the labor force A According to the US Bureau of Labor Statistics, 75% of women 25 through 49 years of age part opate in the labor lorce, 78% of women in that age group are married and 61%are married and participate in the labor force a. What is the probability that a woman in that age group is married or in the labor force? b.What is the probablity that a woman in that age group is marred or in the labor force but not both? c. What is the probability that a woman in that age group is neither married nor in the labor force? d. What is the probability that a woman in that age group is married but not in the labor force? e. Are the events "maried and "in the labor force" independent? Mutually exclusive?Explanation / Answer
75 % women participate in labor force
78% married , 61% married and participate in labor force
(a) P( women is married OR in labor force) = P( married) + P( labor force) - P( married and labor force)
= 0.78 + 0.75 - 0.61 = 0.92
(b) P( married OR labor force but NOT BOTH ) = P( married only ) + P( labor force only )
= ( 0.78-0.61) +(0.75 - 0.61)
= 0.78 + 0.75 - (2*0.61) = 0.31
(c) P( neither married nor labor force) = 1- P( either married or in labor force) = 1- 0.92 = 0.08
(d) P( married but not in labor force) = P( married) - P( both ) = 0.78 - 0.61 = 0.17
(e) Events married and labor force are not mutually exclusive because there are women which are both married and in labor force.
P(married) * P( labor) = 0.78*0.75 = 0.585
P( married and labor force) = 0.61
P( married ) * P( labor) IS NOT EQUAL TO P(married and labor)
Hence the events are DEPENDENT
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