A quality control inspection of smart sensors found that 710\frac{7}{10}107 of the units pass a high-temperature stress test. During a separate evaluation, it was determined that 25\frac{2}{5}52 of the units pass a moisture-resistance test. Among the units that pass the high-temperature stress test, it was found that only 310\frac{3}{10}103 also pass the moisture-resistance test.
Find the probability that a randomly selected sensor from this inspection:
Passes both the high-temperature stress test and the moisture-resistance test.
Does not pass the high-temperature stress test and does not pass the moisture-resistance test.
Determine, giving your reason, whether or not passing the high-temperature stress test and passing the moisture-resistance test are statistically independent.
58 exam-style questions on Edexcel A Level Maths 2.2 Conditional Probability. Each one has a worked solution and a mark scheme showing where the marks go.