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.
200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.