Respuesta :
Answer:
[tex]P(C)=\dfrac{4}{7}[/tex]
Step-by-step explanation:
Given:
I is the event that he has insomnia.
C is the event that he drinks coffee in the morning.
[tex]P(I) = \dfrac{1}{7} , P(C|I) = 1 ,and \:P(C|I^c) = \dfrac{1}{2}[/tex]
[tex]P(I^c)=1-P(I) =1- \dfrac{1}{7}=\dfrac{6}{7}[/tex]
We want to determine the probability that he drinks coffee in the morning, P(C).
Using the Law of Total Probability
[tex]P(C)=P(I)P(C|I)+P(I^c)P(C|I^c)[/tex]
[tex]=\dfrac{1}{7}*1+\dfrac{6}{7}*\dfrac{1}{2}\\=\dfrac{1}{7}+\dfrac{3}{7}\\P(C)=\dfrac{4}{7}[/tex]
The probability that he drinks coffee in the morning is [tex]\dfrac{4}{7}[/tex]
