Respuesta :
Answer:
We have that [tex]B = 0.3[/tex].
So
[tex]0.3 = b + (A \cap B)[/tex]
However, b is a probability, which means that it cannot be negative. So no, P(A ∩ B) cannot be 0.5. It can, at most, be 0.3.
Step-by-step explanation:
Event A:
Probability that a student has a Visa card.
Event B:
Probability that the student has a MasterCard.
We have that:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that a student has a Visa card but not a MasterCard and [tex]A \cap B[/tex] is the probability that a student has both these cards.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
In this problem, we have that:
[tex]A = 0.6, B = 0.3[/tex]
(a) Could it be the case that P(A ∩ B) = 0.5?
We have that [tex]B = 0.3[/tex].
So
[tex]0.3 = b + (A \cap B)[/tex]
However, b is a probability, which means that it cannot be negative. So no, P(A ∩ B) cannot be 0.5. It can, at most, be 0.3.
