A firm has a new plan for workers. 65% of all night-shift workers favored the pl

Question

A firm has a new plan for workers. 65% of all night-shift workers favored the plan. 40% of all female workers favored the plan. 50% of all employees are night workers. 30% of all employees are women. 20% of all night workers are women. Question: If 50% of all male employees favor the plan, what isthe probability that a randomly chosen employee both does not workthe night-shift and does not favor the plan? I was trying to solve this problem by assuming there are 1000workers, but I figure that this approach is very tedious because Ihave to calculate out the number of total male and female, dayworkers and night workers, and stuffs like that. So if anyoneknows a better way to solve it please help me out. A firm has a new plan for workers. 65% of all night-shift workers favored the plan. 40% of all female workers favored the plan. 50% of all employees are night workers. 30% of all employees are women. 20% of all night workers are women. Question: If 50% of all male employees favor the plan, what isthe probability that a randomly chosen employee both does not workthe night-shift and does not favor the plan? I was trying to solve this problem by assuming there are 1000workers, but I figure that this approach is very tedious because Ihave to calculate out the number of total male and female, dayworkers and night workers, and stuffs like that. So if anyoneknows a better way to solve it please help me out.

Explanation / Answer

30% of all employees are women, P (W) = 0.3 40% of all female workers favored the plan. hence 60% of all female workers did not favor the plan. henceProbality of female workers did not favor the plan = 0.6 x 0.3 = 0.18 70% of all employees are men, P (M) = 0.7 50% of all male workers favored the plan. hence 50% of all male workers did not favor the plan. henceProbality of male workers did not favor the plan = 0.5 x 0.7 = 0.35 total probability that the plan was not favoured = 0.18 + 0.35= 0.53 50% of all employees are night workers. hence 50% of allemployees are day workers. hence probability that the plan was not favoured = 0.5 x 0.53= 0.265 40% of all female workers favored the plan. hence 60% of all female workers did not favor the plan. henceProbality of female workers did not favor the plan = 0.6 x 0.3 = 0.18 70% of all employees are men, P (M) = 0.7 50% of all male workers favored the plan. hence 50% of all male workers did not favor the plan. henceProbality of male workers did not favor the plan = 0.5 x 0.7 = 0.35 total probability that the plan was not favoured = 0.18 + 0.35= 0.53 50% of all employees are night workers. hence 50% of allemployees are day workers. hence probability that the plan was not favoured = 0.5 x 0.53= 0.265 70% of all employees are men, P (M) = 0.7 50% of all male workers favored the plan. hence 50% of all male workers did not favor the plan. henceProbality of male workers did not favor the plan = 0.5 x 0.7 = 0.35 total probability that the plan was not favoured = 0.18 + 0.35= 0.53 50% of all employees are night workers. hence 50% of allemployees are day workers. hence probability that the plan was not favoured = 0.5 x 0.53= 0.265 50% of all male workers favored the plan. hence 50% of all male workers did not favor the plan. henceProbality of male workers did not favor the plan = 0.5 x 0.7 = 0.35 total probability that the plan was not favoured = 0.18 + 0.35= 0.53 50% of all employees are night workers. hence 50% of allemployees are day workers. hence probability that the plan was not favoured = 0.5 x 0.53= 0.265

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