There are three research and development projects focusing on the development of three new products A, B, and C. The markets into which the new products are to be launched are identical. However, consumer preference is at present, unknown. A probability assessmen has been undertaken by the Sales Director based upon a recent consumer survey. This has revealed that there is a 1/2 probability that consumers will prefer Product 1, a 1/3 probability that consumers will prefer Product B and a 1/4 probablilty that consumers will prefer Product C. If the company were to launch all three products simultaneously what is the probability that:
a) product A and product B will both be successful?
b) product A, B and C will all be successful?
c) no product will be successful?