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  • Two groups are competing for the positions of the Board of Directors of a corporation.The probabilities that the first and second groups will win are 0.6 and 0.4 respectively.Further, if the first group wins, the probability of introducing a new produc

Two groups are competing for the positions of the Board of Directors of a corporation.The probabilities that the first and second groups will win are 0.6 and 0.4 respectively.Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.

 

 

 

 
 
 
 
 

Answers (1)

Let  E_{1}\Rightarrow events that first group coins
       E_{2}\Rightarrow events that second group coins
       E\Rightarrow now product is introduced
Here p\left ( E_{1} \right )= 0\cdot 6,\: \: p\left ( E_{2} \right )= 0\cdot 4,\; p\left ( \frac{E}{E_{1}} \right )= 0\cdot 7,\; p\left ( \frac{E}{E_{2}} \right )= 0\cdot 3
by Bayes therom, p\left ( \frac{E_{2}}{E} \right )= \frac{p\left ( \frac{E}{E_{2}} \right )p\left ( E_{2} \right )}{p\left ( \frac{E}{E_{1}} \right )p\left ( E_{1} \right )+p\left ( \frac{E}{E_{2}} \right )p\left ( E_{2} \right )}
                                              = \frac{0\cdot 3\times 0\cdot 4}{0\cdot 7\times 0\cdot 6+0\cdot 3\times 0\cdot 4}
             \Rightarrow p\left ( \frac{E_{2}}{E} \right )= \frac{12}{42+12}= \frac{2}{9}

Posted by

Ravindra Pindel

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