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Your friend is addicted to insomnia cookies. She orders Insomnia Cookies at 2 AM 40 percent of the time. When she orders cookies, she sleeps in and misses her 9:30 AM statistics class 75 percent of the time. When she doesn't order cookies, she misses statistics class just 10 percent of the time. This morning she missed class, what is the probability she ordered Insomnia Cookies last night? 1

Respuesta :

Answer:

The probability that the missed class is because she order cookies last night is 0.83.

Step-by-step explanation:

Events:

C: order cookies

NC: not order cookies

M: missed class

Then we know:

P(C)=0.40

P(M|C)=0.75

P(M|NC)=0.10

We need to calculate the probability that the missed class is because she order cookies P(C|M).

According to the Bayes theorem, we have

[tex]P(C|M)=\frac{P(M|C)P(C)}{P(M)}= \frac{P(M|C)P(C)}{P(M|C)P(C)+P(M|NC)P(NC)} \\\\\\P(C|M)=\frac{0.75*0.40}{0.75*0.40+0.10*0.60}=\frac{0.30}{0.30+0.06}=\frac{0.30}{0.36}= 0.83[/tex]

The probability that the missed class is because she order cookies last night is 0.83.