A survey of university students found that 310\displaystyle \frac{3}{10}103 of respondents play a competitive sport. When asked about their sleep patterns, 34\displaystyle \frac{3}{4}43 stated they get at least 8 hours of sleep per night. Of those who get at least 8 hours of sleep, it was found that 1150\displaystyle \frac{11}{50}5011 also play a competitive sport.
Find the probability that a randomly selected student from this survey:
Gets at least 8 hours of sleep and plays a competitive sport.
Does not get at least 8 hours of sleep and does not play a competitive sport.
Determine, giving your reason, whether or not getting at least 8 hours of sleep and playing a competitive sport are statistically independent.
