Question 4.7: Product Launch Success Study A company plans to launch a new......

Let S = the product launch is a success      Y = Market research is positive (predicts product success)

F = the product launch is a failure      N = Market research is negative (predicts product failure)

From the management scenario, the following probabilities can be derived:

S is the prior event – ‘product success’.      P(S) = 0.4 (prior probability) and P(F) = 0.6

New information from market research results in the following revised probabilities:

P(Y|S) = 0.8        and         P(Y|F) = 0.3

Required to find P(S|Y) – the posterior probability

i.e. the probability of a successful launch (S) given that the market research findings are positive (Y) for a successful launch.

P(S|Y) = P(S and Y) / P(Y)                     (Bayes’ Theorem)

Now:         P(S and Y) = P(Y|S) × P(S) = 0.8 × 0.4 = 0.32 (multiplication rule)

P(F and Y) = P(Y|F) × P(F) = 0.3 × 0.6 = 0.18 (multiplication rule)

and        P(Y) = P(S and Y) + P(F and Y) = 0.32 + 0.18 = 0.50

Then        P(S|Y) = 0.32|0.50 = 0.64

These probabilities can be computed and displayed in a probability tree as follows:

Interpretation

There is a 64% chance that the product will be successfully launched given that it has a positive market research report.