Three oil companies, A, B and C, are exploring for oil in an area. The probabilities that they will discover oil are, respectively, 0.40, 0.60 and 0.20. If B discovers oil, the probability that A will also discover oil is increased by 20%. Assume that the chance of C discovering oil is independent of A and B. i) What is the probability that oil will be discovered in the area by one or more of the three companies?
ii) If oil is discovered in the area, what is the probability that it will be discovered by company C?

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

step-by-step explanation:

hope it

step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)