The editor of a major textbook publishing company is trying to decide whether to publish a proposed new business statistics textbook. Previous textbooks published indicate that 10% are huge successes, 20% are modest successes, 40% break even, and 30% are losers. However, before a publishing decision is made, the book will be reviewed. In the past, 99% of the huge successes received favourable reviews, 70% of the moderate successes received favourable reviews, 40% of the break-even books received favourable reviews, and 20% of the losers received favourable reviews.
a) What proportion of textbooks receive favourable reviews?
b) If the proposed text receives a favourable review, what is the probability that it will be a moderate success?