Question

An oil company is drilling for oil at three sites. According to geological tests, the probabilities of

finding oil the sites is at these three sites are 0.30, 0.15, and 0.20, respectively. The presence of oil at any one of presumed to be independent of the presence of oil at any of the other sites.

What is the probability of finding oil at all three of the sites?
What is the probability of not finding oil at any of the sites?
What event would be the complement of finding oil at all three sites? What event would be the complement of not finding oil at any of the sites?

Answer 1

Answer:

Step-by-step explanation:

Given

Probability of finding oil at site 1 is 0.30

Probability of finding oil at site 2 is 0.15

Probability of finding oil at site 3 is 0.20

Probability of Finding oil at all three sites

i.e. oil is present in all three sites simultaneously

$=0.3\times 0.15\times 0.20=0.009$

Probability of not finding oil at any of these sites$=(1-0.3)\cdot (1-0.15)\cdot (1-0.2)=0.476$

Complement of Finding oil at all three sites is equivalent to not finding the oil at all three sites

i.e. $A'\cap B'\cap C'$

Complement of not finding oil at any of the sites is equivalent to probability of finding oil at any of the given sites

$A\cup B' \cup C'$ or

$'\cup B \cup C'$ or

$A'\cup B' \cup C$