Respuesta :
Answer:
The probability that a randomly chosen death is a white person who died of diabetes is of 0.0241 = 2.41%.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: The person is white
Event B: Died of diabeters.
Of people who died in the United States in recent years, 86% were white
This means that [tex]P(A) = 0.86[/tex]
Diabetes caused 2.8% of deaths among whites
This means that [tex]P(B|A) = 0.028[/tex]
The probability that a randomly chosen death is a white person who died of diabetes is about:
This is [tex]P(A \cap B)[/tex]. So
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)*P(A) = 0.028*0.86 = 0.0241[/tex]
The probability that a randomly chosen death is a white person who died of diabetes is of 0.0241 = 2.41%.
