Functional Robotics Corporation buys electrical controllers from a Japanese supplier. The company's treasurer thinks that there is probability 0.2 that the dollar will fall in value against the Japanese yen in the next month. The treasurer also believes that if the dollar falls there is probability 0.6 that the supplier will demand renegotiation of the contract. What probability has the treasurer assigned to the event that the dollar falls and the supplier demands renegotiation

Question

Mueller

Mathematics

10 December, 19:18

Functional Robotics Corporation buys electrical controllers from a Japanese supplier. The company's treasurer thinks that there is probability 0.2 that the dollar will fall in value against the Japanese yen in the next month. The treasurer also believes that if the dollar falls there is probability 0.6 that the supplier will demand renegotiation of the contract. What probability has the treasurer assigned to the event that the dollar falls and the supplier demands renegotiation

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Tristian Nicholson · Answer 1

the probability is 0.12 (12%)

Step-by-step explanation:

Defining the following events F = the dollar falls in value against the Japanese yen in the next month and the event R=the supplier will demand renegotiation of the contract, then we can apply conditional probability using the theorem of Bayes:

P (R∩F) = P (F) * P (R/F)

where

P (R∩F) = probability that the supplier will demand renegotiation of the contract and the dollar falls in value against the Japanese yen in the next month

P (R/F) = probability that the supplier will demand renegotiation of the contract if the dollar falls in value against the Japanese yen in the next month

then replacing values

P (R∩F) = P (F) * P (R/F) = 0.2 * 0.6 = 0.12

therefore the probability is 0.12 (12%)