Probability

(a) Events A and B are such that P(A) = 0.5, P(B | A) = 0.3 and P(B | A') = 0.6. (i) Draw a tree diagram to show this information. (ii) Find P(B). (iii) Find P(A | B). (iv) Determine whether A and B are independent. (b) For a random sample of 20 students, the product moment correlation coefficient between hours of revision and test score is 0.42. Test, at the 5% level, whether there is positive correlation in the population. (One-tailed critical value: 0.3783.)