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According to a recent​ study, 9.3​% of high school dropouts are​ 16- to​ 17-year-olds. In​ addition, 6.3​% of high school dropouts are white​ 16- to​ 17-year-olds. What is the probability that a randomly selected dropout is​ white, given that he or she is 16 to 17 years​ old?

Respuesta :

JeanaShupp

Answer:  [tex]\dfrac{21}{31}[/tex]

Step-by-step explanation:

Let A represents the event that high school dropouts are ​16- to​ 17-year-olds and B be the event that high school dropouts are ​white.

Given : The probability of high school dropouts are​ 16- to​ 17-year-olds :[tex]P(A)=0.093[/tex]

The probability of of high school dropouts are white​ 16- to​ 17-year-olds :

[tex]P(A\cap B)=0.063[/tex]

Then , the conditional  probability that a randomly selected dropout is​ white, given that he or she is 16 to 17 years​ old is given by :-

[tex]P(B|A)=\dfrac{P(A\cap B)}{P(A)}\\\\\Rightarrow\ P(B|A)=\dfrac{0.063}{0.093}=\dfrac{21}{31}[/tex]

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