Question

Two groups are competing for the position on the board of directors of a corporation. The probabilities that the first and the 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.​

Answer 1

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Step-by-step explanation:

P (G₁) = 0.6 P (G₁₁) = 0.4

Let E is the event of introducing new product then

P (E/G₁) = 0.7 P( E/G₁₁ ) = 0.3

To find P(G₁₁ / E)

Using Baye's Theorem, we get

P (G₁₁/E) = P(G₁₁).P(E/G₁₁) / P(G₁₁) . P(E/G₁) + P(G₁₁).P(E/G₁₁)

= 0.4 × 0.3 / 0.6 × 0.7 + 0.4 × 0.3

$\frac{0.12}{0.42 + 0.12} = \frac{12}{54} = \frac{2}{9}$

GOOD LUCK !!

Answer 2

$\huge \mathtt { \underline{ \underline\red{ \red{A{ \pink{N{ \blue{S{ \green{W{ \purple{E{ \orange{R { \red{~ :-}}}}}}}}}}}}}}}}$

Step-by-step explanation:

P (G₁) = 0.6 P (G₁₁) = 0.4

Let E is the event of introducing new product then

P (E/G₁) = 0.7 P( E/G₁₁ ) = 0.3

To find P(G₁₁ / E)

Using Baye's Theorem, we get

P (G₁₁/E) = P(G₁₁).P(E/G₁₁) / P(G₁₁) . P(E/G₁) + P(G₁₁).P(E/G₁₁)

= 0.4 × 0.3 / 0.6 × 0.7 + 0.4 × 0.3

$\frac{0.12}{0.42 + 0.12} = \frac{12}{54} = \frac{2}{9}$

GOOD LUCK !!