In order to study the relationship between the amount of sleep a student gets and his or her school performance, a researcher collected data from 120 students. The two-way frequency table shows the number of students who passed and failed an exam and the number of students who got more or less than 6 hours of sleep the night before.
The probability that a student who failed the exam got less than 6 hours of sleep can be calculated as:
Let,
L be the event of getting less than 6 hours of sleep
F be the event of failing the exam.
Then,
P(L and F) = n(L∩F) ÷ n(F)
= (10 ÷ 18) × 100%
= 5 ÷ 9 × 100%
= 55.55%