6 points 8. The zombie apocalypse has arrived! Luckily, you live in a remote pop

Question

6 points 8. The zombie apocalypse has arrived! Luckily, you live in a remote population has become zombies. As the town biologist, you have created a new test that tries to determine if a person is a zombie. Sadly, the test isn't perfect. If a person is not a zombie, it inaccurately claims they are (!) about 4% of the time. If the person is a zombie, the test will always get this cont town, and only 1% of the ect. , suppose a random person has tested positive. After learning this info, your friend bets you $400 the n actually is a zombie. You disagree and think the person is not a zombie. You're willing to bet a dollars. If you're right, you win his $400 dollars (and your r back); if you're wrong, you lose r dollars (and he gets his $400 back). What should z be if you want the bet to be even (i.e., you won't win or lose money on average)?

Explanation / Answer

Answer:

Acc. to the test: If the person is not a zombie, it inaccurately claims that it is a zombie 4% of a time.

As you are claiming that the person is not a zombie and test says that it is, the probability that you are right = 4% = 0.04

Probability to win = 0.04
Probability to lose = 0.96

Win Value = 400 + x

Lose Value = -x

If the bet has to be even, E(bet) = 0

(400 + x) * 0.04 + (-x) * 0.96 = 0

16 + 0.04x - 0.96x = 0

16 = 0.92x

x = 17.39

Hence, he has to bet $17.39 dollars for the bet to be even.

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