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May 23rd, 2018, 04:42 PM   #1
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Probability 2

Hello

I solved the exercise already, but with formulas of probability and table, in other words, in easy way.
This time, I want to solve it with using algebra, I'm interested in increasing my thinking and enriching algebra.
So can you tell me please whether my answers are correct? If they are not, can you help/fix please?

The exercise:
The ground is divided into 3 areas: A, B and C.
There is oil in all areas (A, B and C).
When people will want to drill and find oil, 50% of chance that they will go to area A, 40% of chance that they will go to area B and 10% of chance that they will go to area C.
The probability of finding oil in area A is 0.03, the probability of finding oil in area B is 0.1 and the probability of finding oil in area C is 0.2.

a) In a certain drilling, what is the chance of finding oil?

b) Oil was found in a certain drilling, what is the probability that the area is B?

c) In another drilling, oil was found, but it was discovered that the area is not B:
(1) What is the probability that the area is C?
(2) What is the probability of finding oil now?

My answers:
a) Area A is 50%, it means: 100%/2, and the probability is 0.03, then: 0.03/2 = 0.015.
Area B is 40%, it means: 100%/2.5, and the probability is 0.1, then: 0.1/2.5 = 0.04.
Area C is 10%, it means: 100%/10, and the probability is 0.2, then: 0.2/10 = 0.02.
0.015 + 0.04 + 0.02 = 0.075.

b) Oil was found, so we will only relate to oil, then: 0.04/(0.015+0.04+0.02) = 0.533.

c.1) Oil was found and we have only two areas (A and C), then: 0.02/(0.015+0.02) = 0.571.
c.2) Oil was found and we have only two areas (A and C), then: 0.015+0.02 = 0.035.


I know that I can compare answers (because I solved it already), but the answers aren't important, the ways to a solution are.
If you didn't understand something, tell me please.
Sorry for my bad English.


Thanks!

Last edited by greg1313; May 24th, 2018 at 07:27 AM.
IlanSherer is offline  
 
May 23rd, 2018, 04:59 PM   #2
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It all looks fine to me. As long as you understand

$P[A|B]P[B] = P[B|A]P[A]$

You should be good to go. Everything can be derived from that.
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May 24th, 2018, 04:23 AM   #3
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Without using formulas:

Imagine repeating this scenario 1000 times. 500 times they drill in A, 400 times in B, and 100 times in C. 0.05 X 500= 15 times they find oil in A, 0.1 X 400= 40 times they find oil in B, and 0.2 X 100= 20 times they find oil in C.

a) In a certain drilling, what is the chance of finding oil?
Out of 1000 times drilling they found oil a total of 15+ 40+ 20= 75 times. The probability of finding oil is 75/1000= 7.5%.

b) Oil was found in a certain drilling, what is the probability that the area is B?
They found oil 75 times, 40 of those times drilling in B. Given that they found oil, the probability that it was in B is 40/75= 8/15.

c) In another drilling, oil was found, but it was discovered that the area is not B:
(1) What is the probability that the area is C?
They found oil, not in B, 15+ 20= 35 times. 20 times that was in C. Given that they found oil, not in B, the probability that it was in C is 20/35= 4/7.

(2) What is the probability of finding oil now?
Assuming that the "now" here means "not in B", they drilled in A and C a total of 500+ 100= 600 times and found oil 15+ 20= 35 times. The probability they find oil In A or C is 35/600= 7/120.

(That last interpretation of "now" is not clear to me. Problem (c) says "oil was found"!)
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