In a random sample of 200 students, 55% indicated they have full-time jobs, while the other 45% have part-time jobs. Fifty of the 90 male students surveyed have a full-time job, and 60 of the females surveyed have a full-time job. What is the probability that a randomly selected student is female given they have a part-time job?

Answer:The probability is [tex]\frac{5}{9}[/tex]Step-by-step explanation:The total number of students are 200.number of full timers is 110 and number of part timers is 90.number of male students is 90 and number of female students is 110.Let the probability of part timers be P(B).P(B) = [tex]\frac{90}{200}[/tex] = [tex]\frac{9}{20}[/tex]Let the probability of female part timers be P(A)P(A) = [tex]\frac{50}{200} = \frac{5}{20}[/tex]now, the final probability is = [tex]\frac{P(A)}{P(B)}[/tex]=[tex]\frac{5/20}{9/20} = \frac{5}{9}[/tex]