Answer:
P(A and B) is greater than 1 is never happened ⇒ C
Step-by-step explanation:
Two events are independent if the result of the second event is not affected by the result of the first event
If A and B are independent events, the probability of both events is the product of the probabilities of the both events P (A and B) = P(A) · P(B)
∵ The probability of any event is less than 1
∵ P(A) < 1
∵ P(A) > [tex]\frac{1}{2}[/tex]
- That means P(A) is greater than half and less than 1
∴ [tex]\frac{1}{2}[/tex] < P(A) < 1
∵ P(B) < 1
∵ P(B) > [tex]\frac{1}{2}[/tex]
- That means P(B) is greater than half and less than 1
∴ [tex]\frac{1}{2}[/tex] < P(B) < 1
∵ P(A and B) = P(A) . P(B)
- Remember the product of any fractions less than 1 is less than 1
∴ [tex]\frac{1}{4}[/tex] < P(A) . P(B) < 1
- That means any expression equals to P(A) . P(B) must be greater
than [tex]\frac{1}{4}[/tex] and less than 1
∴ [tex]\frac{1}{4}[/tex] < P(A and B) < 1
∴ P(A and B) is greater than 1 is never happened
