Final answer:
To calculate the probability that a randomly selected worker is both female and employed, you multiply the percentage of the workforce that is female (58%) by the employment rate for women (91%). This equals 52.78%, which, as a decimal, is 0.5278, but this does not match the provided options.
Step-by-step explanation:
The question asks what is the probability that a randomly selected worker is both female and employed given that the unemployment rate is 10% for eligible men and 9% for eligible women, with men comprising 42% of the eligible workforce.First, we determine the percentage of the workforce that is female:100% - 42% (male workforce) = 58% (female workforce).Then, we calculate the employment rate for women:100% - 9% (unemployment rate for women) = 91% (employment rate for women).Now, we find the probability that a randomly selected worker is both female and employed by multiplying the percentage of the workforce that is female by the employment rate for women:58% * 91% = 52.78%.Converting this percentage to a decimal to match the answer choices gives us 0.5278, which is not among the options provided. So let's look at the calculation in terms of the probability:0.58 (female workforce) * 0.91 (employment rate for women) = 0.5278However, the student made an error. The probability needs to be multiplied by 100 to convert it into a percentage.
This step was missed:0.5278 * 100 = 52.78The correct options, which are in decimal form without the percentage sign, do not include this answer. We may need to double-check our calculations or the options provided.To find the probability that a randomly selected worker is both female and employed, we need to consider the percentage of eligible women who are employed.Given that the unemployment rate for eligible women is 9.0%, it means that the employment rate for eligible women is 100% - 9.0% = 91.0%.Since 42% of the eligible workforce consists of men and the remaining 58% consists of women, the probability that a randomly selected worker is both female and employed is 0.58 * 0.91 = 0.5278, which is approximately 0.528.