Die A is rolled 50 times and a 6 is scored 4 times, while a 6 is obtained 10 times when die B is rolled 50 times.
(a) Construct a two-sided 99% confidence interval for the difference in the probabilities of scoring a 6 on the two dice.
(b) Calculate a p-value for the two-sided null hypothesis that the two dice have equal probabilities of scoring a 6.
(c) What would your answers be if die A produced a 6 40 times in 500 rolls and die B produced a 6 100 times in 500 rolls?