Final answer:
To determine the fraction of students who watched and recorded a reality show, multiply the fractions representing each event: 2/3 of students watched TV, 3/8 of those watched a reality show, and 1/4 of those recorded it, resulting in 1/16 of all students.
Step-by-step explanation:
To find the fraction of the students in Rick's class who watched and recorded a reality TV show, we need to multiply the probabilities (fractions) for each sequential event, because probabilities of independent events are multiplied to find the joint probability. First, 2/3 of the students watched television. Next, out of those students, 3/8 watched a reality show. And finally, 1/4 of those who watched the reality show recorded it.
The calculation for the fraction of all students who watched and recorded the show is:
(2/3) × (3/8) × (1/4) = (2 × 3 × 1) / (3 × 8 × 4)
When we multiply the numerators together and the denominators together, it simplifies to:
6 / 96
Which can then be reduced by dividing both the numerator and the denominator by 6:
1/16
So, 1/16 of the students in Rick's class watched and recorded a reality TV show.