For Exercises 53–58, use the Multiplication Rule to find the indicated probability.

Question 5.271

58. Thirty percent of the statistics students at a particular college have taken advantage of the college tutoring program. After doing so, 80% of them received a higher score on the next exam. Find the probability that a statistics student has taken advantage of the college tutoring program and has received a higher score on the next exam.

The National Center for Education Statistics reports the following statistics for surveys of 12,320 female college students and 9,184 male college students:

  • 36% of females work 16–25 hours per week
  • 38% of males work 16–25 hours per week

A random sample of college students is taken. Define the following events:

  • F1: 1st draw is a female who works 16–25 hours
  • F2: 2nd draw is a female who works 16–25 hours
  • M1: 1st draw is a male who works 16–25 hours
  • M2: 2nd draw is a male who works 16–25 hours