Consider the well failure data given below. Let A denote the event that the geol
ID: 3374763 • Letter: C
Question
Consider the well failure data given below. Let A denote the event that the geological formation of a well has more than 1000 wells, and let B denote the event that a well failed Geological Formation Group Gneiss Granite Loch raven schist Mafic Marble Prettyboy schist Other schists Serpentine Wells Failed Total 180 1285 2 28 443 3733 14 363 29 309 60 1403 46 933 3 39 Determine P(A) Round your answer to four decimal places (e.g. 98.7654) P(A) Determine P(B) Round your answer to four decimal places (e.g. 98.7654) Determine P(An B) Round your answer to four decimal places (e.g. 98.7654)Explanation / Answer
Answer
First we need to find the sum of Failed and sum of failed and total
Sum of failed = (180+2+443+14+29+60+46+3) = 777
Sum of failed + total = 777+(1285+28+3733+363+309+1403+933+39) = 8870
(i) P(A) = (favorable outcome)/(total outcome)
Favorable outcome = 1285+3733+1403 = 6421
And total outcome = 8870
So, P(A) = 6421/8870 = 0.7239
(ii) P(B) = (favorable outcome)/(total outcome)
Favorable outcome = 777
And total outcome = 8870
So, P(A) = 777/8870 = 0.0876
(iii) Event A and B are mutually exclusive because there is no case where the geographical formation of a well has more than 1000 wells and that is a well failed
So, P(A) and P(B) are mutually exclusive
Thus, we can write it as
P(A or B) = P(A)+P(B) = 0.7239 +0.0876 = 0.8115
Now, we need to find P(A and B)
Using the formula
P(A and B)= P(A)+P(B) – P(A or B) = 0.7329 + 0.0876 – 0.8115 = 0.8115 – 0.8115 = 0
So, Required probability P(A n B) = 0 because there is no common event for A and B events
A and B are not independent because P(A n B) is not equal to product of P(A) and P(B)
Means P(A n B) = 0 and P(A)*P(B) = 0.7239*0.0876 = 0.0634
So, it is clear that 0 is not equal to 0.0634
So, A and B are not independent event