Question

slader An electronics company is planning to introduce a new camera phone. The company commissions a marketing report for each new product that predicts either the success or failure of the product. Of new products introduced by the company, 60% have been successes. Furthermore, 70% of their successful products were predicted top be successes, while 40% of failed products were predicted to be successes. Find the probability that this new camera phone will be successful if its success has been predicted.

Answer 1

Answer: Our required probability is 0.7241.

Step-by-step explanation:

Since we have given that

Probability that new product have been successes P(S) = 60%

Probability that new product have not been successes P(F) = 40%

Probability that their successful products were predicted to be successes = P(A|S)=70%

Probability that their failed products were predicted to be successes =P(A|F) = 40%

So, Probability that this new camera phone will be successful if its success has been predicted is given by

$P(S|A)=\dfrac{P(S).P(A|S)}{P(S).P(A|S)+P(F).P(A|F)}\\\\P(S|A)=\dfrac{0.7\times 0.6}{0.7\times 0.6+0.4\times 0.4}\\\\P(S|A)=0.7241$

Hence, our required probability is 0.7241.