Math

QuestionAn oil firm has a 10%10\% success rate. Find the probability of hitting oil on the first well and missing the second, and at least one hit in two wells.

Studdy Solution

STEP 1

Assumptions1. The firm hits oil or gas on10% of its drillings. . The firm drills two wells.
3. The events are independent, meaning the outcome of the first drilling does not affect the outcome of the second drilling.
4. The probabilities of all possible outcomes must add up to1.

STEP 2

First, let's find the probability that the company will hit oil or gas on the first drilling and miss on the second. This is event 2_{2}, but we don't know its probability yet. However, we can calculate it using the fact that the events are independent. The probability of independent events is the product of their individual probabilities.
(E2)=(Hit on first drilling)×(Miss on second drilling)(E_{2}) =(\text{Hit on first drilling}) \times(\text{Miss on second drilling})

STEP 3

We know that the probability of hitting oil or gas is10%, or0.1. Therefore, the probability of missing is1 -0.1 =0.9. Let's substitute these values into the equation.
(E2)=0.1×0.9(E_{2}) =0.1 \times0.9

STEP 4

Calculate the probability of event 2_{2}.
(E2)=0.1×0.9=0.09(E_{2}) =0.1 \times0.9 =0.09

STEP 5

Now, let's find the probability that the company will hit oil or gas on at least one of the two drillings. This is the sum of the probabilities of events 1_{1}, 2_{2}, and 3_{3}.
(Hit at least once)=(E1)+(E2)+(E3)(\text{Hit at least once}) =(E_{1}) +(E_{2}) +(E_{3})

STEP 6

Substitute the known probabilities into the equation.
(Hit at least once)=0.01+0.09+0.09(\text{Hit at least once}) =0.01 +0.09 +0.09

STEP 7

Calculate the probability of hitting oil or gas at least once.
(Hit at least once)=0.01+0.09+0.09=0.19(\text{Hit at least once}) =0.01 +0.09 +0.09 =0.19The probability that the company will hit oil or gas on the first drilling and miss on the second is0.09, and the probability that the company will hit oil or gas on at least one of the two drillings is0.19.

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