Question

A company that explores for oil in the ocean is considering two new sites, A and B. The exploration will take the entire year. The company estimates the probability of finding oil is 0.6 at site A and 0.84 at site B. The sites are far enough apart so that whether or not oil is found at one site, is independent of its being found at the other.

Answer 1

Answer:

Step-by-step explanation:

Hello!

There are two sites A and B,

Be the events A: finding oil in site Awith probability P(A)= 0.6

and B: finding oil in B with probability P(B)= 0.84

A and B are independent (there cannot be found oil of A in B and vice versa)

Remember, two events are independent when the occurrence of one of them doesn't modify the probability of occurrence of the other one in two repetitions of the experiment.

1) Find the probability that oil is found at both sites (round your answer to 2 decimal places)

If there is oil in both sites then event A and B are observed, symbolically:

P(A∩B)

Since both events are independent, the probability of the intersection of both events is equal to the product of each probability so:

P(A∩B)= P(A)*P(B)= 0.6*0.84= 0.504

2) Find the probability that oil is found at only one of the sites (round your answer to 2 decimal places)

In this case, you have two situations in which the statement can occur:

> "finding oil in A" and "not finding oil in B"

-or-

> "not finding oil in A" and "finding oil in B"

Be A' the complementary event of A, i.e. "not finding oil in region A", with probability P(A')= 1 - P(A)= 1 - 0.6= 0.4

And B' the complementary event of B, i.e. "not finding oil in region B", with probability P(B')= 1 - P(B)= 1 - 0.84= 0.16.

You can symbolize these two possible occurrences as:

Remember that "and" indicated intersection between two events, symbolized ∩, and "or" indicates the union between two events, symbolized ∪.

P((A∩B')∪(A'∩B))= P(A∩B') + P(A'∩B)= [P(A)*P(B')]+[P(A')*P(B)]= (0.6*0.16)+(0.4*0.84)= 0.432

I hope it helps!