Respuesta :
Answer:
Step-by-step explanation:
i )
the probability that oil will be discovered in the area by one or more of the three companies = probability of oil to be discovered by one company + probability that oil will be discovered by two companies + probability that oil will be discovered by three companies.
probability of oil to be discovered by one company = .40 x .40 x .80 + .60 x .60 x .80 + .60 x .40 x .20 = .128 + .288 + .048 = .464
probability that oil will be discovered by two companies = probability to be discovered by A and B and not discovered by C + probability to be discovered by A and C and not discovered by B + probability to be discovered by B and C and not discovered by A
= .40 x .80 x .80 + .40 x .20 x .40 + .60 x .20 x .60
= .256 + .032 + .072
= .36
probability that oil will be discovered by three companies.
= .40 x .60 x .20 = .048
Total probability = .464 + .36 + .048 = .872
ii )
Probability of discovery by C = Probability by C and not by A and B + Probability by C and A and not by B + Probability by C and B and not by A
+ Probability by A , B and C .
= .20 x .6 x .4 + .20 x .40 x .40 + .20 x .60 x .60 + .40 x .60 x .20
= .048 + .032 + .072 + .048
= .20
If oil is discovered in the area, what is the probability that it will be discovered by company C = .20 / .872
= .23
The probability that oil will be discovered in the area by one or more of the three companies is 86.24%, and if oil is discovered in the area, the probability that it will be discovered by company C is 16.66%.
Given that three oil companies, A, B and C, are exploring for oil in an area, and the probabilities that they will discover oil are, respectively, 0.40, 0.60 and 0.20, and if B discovers oil, the probability that A will also discover oil is increased by 20%, assuming that the chance of C discovering oil is independent of A and B, to determine 1) what is the probability that oil will be discovered in the area by one or more of the three companies, and 2 ) if oil is discovered in the area, what is the probability that it will be discovered by company C, the following calculations must be made:
1)
- The discovery probabilities of 1, 2 or 3 companies must be added.
- (0.40 x 0.40 x 0.80 + 0.60 x 0.60 x 0.80 + 0.60 x 0.40 x 0.20) + (0.48 x 0.60 x 0.80 + 0.40 x 0.60 x 0.20 + 0.60 x 0.60 x 0.20) + (0.40 x 0.60 x 0.20) + (0.40 x 0.60 x 0.20)
- (0.128 + 0.288 + 0.048) + (0.2304 + 0.048 + 0.072) + 0.048 = X
- 0.464 + 0.3504 + 0.048 = X
- 0.8624 = X
2)
- 1.20 = 100
- 0.20 = X
- 0.20 x 100 / 1.20 = X
- 20 / 1.20 = X
- 16.66 = X
Therefore, the probability that oil will be discovered in the area by one or more of the three companies is 86.24%, and if oil is discovered in the area, the probability that it will be discovered by company C is 16.66%.
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