Eight tyres of different brands are ranked from 1 to 8 (best to worst) according to mileage performance. If four of these tyres are selected at random:

a) Find the probability that the best tyre among those selected is actually ranked third among the original eight

b) Find the probability that the worst tyre among those selected is actually ranked seventh among the original eight

c) Find the probability that the best tyre and the worst tyre among these selected are actually ranked third and seventh respectively among the original eight. Are these two events independent

d) Let random variable, R, represent the range of the original ranks in the four tyres selected. Thus in part (c), R = 7-3 = 4. determine the probability distribution for R and display in the form of a table

e) Graph the probability mass function and cumulative distribution functions for R