Question
If A and B are any events, the property that is not always true is: a) 0 β€ π(π΄ β© π΅) β€ 1 b) π(Ξ©) = 1 c) π(π΅) = 1 β π(π΅π) d) π(β ) = 0 e) π(π΄ βͺ π΅) = π(π΄) + π(π΅)
242
likes1212 views
Answer to a math question If A and B are any events, the property that is not always true is: a) 0 β€ π(π΄ β© π΅) β€ 1 b) π(Ξ©) = 1 c) π(π΅) = 1 β π(π΅π) d) π(β ) = 0 e) π(π΄ βͺ π΅) = π(π΄) + π(π΅)
Hank
4.8105 Answers
To determine the property that is not always true, let's analyze each option:
a) 0 β€ π(π΄ β© π΅) β€ 1
This property is always true because the probability of an intersection of two events can range from 0 (if the events are mutually exclusive) to 1 (if the events are identical).
b) π(Ξ©) = 1
This property is always true because the probability of the sample space, Ξ©, which represents all possible outcomes, is always equal to 1.
c) π(π΅) = 1 β π(π΅π)
This property is always true because the probability of an event and the probability of its complement add up to 1.
d) π(β ) = 0
This property is always true because the probability of an empty set, represented by β , is always equal to 0.
e) π(π΄ βͺ π΅) = π(π΄) + π(π΅)
This property is not always true. It holds true only if the events A and B are mutually exclusive. If the events are not mutually exclusive, then we need to subtract the probability of their intersection (π(π΄ β© π΅)) from the sum of their probabilities.
Therefore, the property that is NOT always true is e) π(π΄ βͺ π΅) = π(π΄) + π(π΅).
Answer: e) π(π΄ βͺ π΅) = π(π΄) + π(π΅)
a) 0 β€ π(π΄ β© π΅) β€ 1
This property is always true because the probability of an intersection of two events can range from 0 (if the events are mutually exclusive) to 1 (if the events are identical).
b) π(Ξ©) = 1
This property is always true because the probability of the sample space, Ξ©, which represents all possible outcomes, is always equal to 1.
c) π(π΅) = 1 β π(π΅π)
This property is always true because the probability of an event and the probability of its complement add up to 1.
d) π(β ) = 0
This property is always true because the probability of an empty set, represented by β , is always equal to 0.
e) π(π΄ βͺ π΅) = π(π΄) + π(π΅)
This property is not always true. It holds true only if the events A and B are mutually exclusive. If the events are not mutually exclusive, then we need to subtract the probability of their intersection (π(π΄ β© π΅)) from the sum of their probabilities.
Therefore, the property that is NOT always true is e) π(π΄ βͺ π΅) = π(π΄) + π(π΅).
Answer: e) π(π΄ βͺ π΅) = π(π΄) + π(π΅)
Frequently asked questions (FAQs)
What is the result of evaluating f(x) = 2x^2 - 4x + 1 for x = 3?
+
What is the value of f(10) when f(x) = log x and f(x) = ln x?
+
Math Question: Solve for x in the linear function f(x)=x-2. What is the value of x when f(x)=5?
+
New questions in Mathematics