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Your friend tossed a fair coin when you weren’t around. She has a habit of messing with you every once in a while, and so there is a 1/3 chance that she will lie to you about the result of the coin toss (report heads as tails and tails as heads), and 2/3 chance that she will tell you the true result of the coin toss. Suppose she claims that the coin toss resulted in heads. What’s the probability that she’s lying?

Respuesta :

Answer:

Step-by-step explanation:

Given that your friend tossed a fair coin when you weren’t around.

Let A be the event that she said the outcome is head

B1 = Event she lied and B2 = Event she did not lie

[tex]P(B1) = \frac{1}{3}    \\ P(B2) \frac{2}{3}[/tex]

P(AB1) = [tex]\frac{1}{2} *\frac{1}{3} =\frac{1}{6}[/tex]

P(AB2) = [tex]\frac{2}{3} \frac{1}{2} =\frac{2}{6}[/tex]

Required probability = P(B1/A)=[tex]\frac{P(B1A)}{P(B1A)+P(B2A)} \\=\frac{\frac{1}{6} }{\frac{1}{6}+\frac{2}{6}} \\=\frac{1}{3}[/tex]

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