You are given that P(A) = 0.5 and P(A ∪ B) = 0.7. Student 1 assumes that A and B are independent and calculates P(B) based on that assumption. Student 2 assumes that A and B are mutually exclusive and calculates P(B) based on that assumption. Find the absolute difference between the tw

The absolute difference between the two calculations is 0.2

Step-by-step explanation:

Student 1

When the events do not affect each other, they are known as independent events. That is, two events are independent if the result of the second event is not affected by the result of the first event.

When two events are independent, the probability that A and B occur is equal to the product of the probability that A occurs and the probability that B occurs. Then:

P(A∩B)= P(A)*P(B)

The probability of the opposite event is equal to 1 minus the probability of the  event. So in this case you have:

P(A'∩B')= 1 - P(A∪B)

Being P(A∪B)= 0.7, then:

P(A'∩B')= 1 -0.7

P(A'∩B')= 0.3

Being P(A)= 0.5 and P(A'), so

0.3= 0.5*P(B)

P(B')=0.6

Being P(B)= 1 - P(B') so P(B)= 1 - 0.6 and you get P(B)=0.4

Student 2

Two events are mutually exclusive when both cannot occur simultaneously. In other words, two events A and B are incompatible or mutually exclusive when they have no element in common. This is: P(A∩B)= 0

Being P(A∪B) =P(A) + P(B) - P(A∩B), P(A)=0.5 and P(A∪B)= 0.7, you get:

0.7=0.5 + P(B) -0

Solving:

0.7=0.5 + P(B)

0.7 - 0.5 = P(B)

0.2 = P(B)

Finally the absolute difference between the two calculations can be calcutated as:

|0.4 - 0.2|= 0.2

The absolute difference between the two calculations is 0.2

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step-by-step explanation: