6) 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 assessment has been undertaken by the Sales Director based upon a recent consumer survey. This has revealed that there is a ½ probability that consumers will prefer Product A, a 1/3 probability that consumers will prefer Product B and a ¼ probability 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?

the fractions don't add to 100%

To find the probabilities in this scenario, we can simply multiply the individual probabilities together.

a) To find the probability that both Product A and Product B will be successful, we need to multiply the probabilities of each product being preferred. The probability of consumers preferring Product A is 1/2 and the probability of consumers preferring Product B is 1/3. So the probability of both A and B being successful is:

Probability (A and B) = Probability (A) * Probability (B) = (1/2) * (1/3) = 1/6

Therefore, the probability that both Product A and Product B will be successful is 1/6.

b) To find the probability that all three products A, B, and C will be successful, we need to multiply the probabilities of each product being preferred. The probability of consumers preferring Product A is 1/2, the probability of consumers preferring Product B is 1/3, and the probability of consumers preferring Product C is 1/4. So the probability of all three products being successful is:

Probability (A and B and C) = Probability (A) * Probability (B) * Probability (C) = (1/2) * (1/3) * (1/4) = 1/24

Therefore, the probability that all three products will be successful is 1/24.

c) To find the probability that no product will be successful, we need to consider the complementary event where none of the products are successful. The probability of consumers not preferring Product A is 1 - 1/2 = 1/2. Similarly, the probability of consumers not preferring Product B is 1 - 1/3 = 2/3, and the probability of consumers not preferring Product C is 1 - 1/4 = 3/4. So the probability of no product being successful is:

Probability (None of A, B, or C) = Probability (not A) * Probability (not B) * Probability (not C) = (1/2) * (2/3) * (3/4) = 1/4

Therefore, the probability that no product will be successful is 1/4.