According to Chinese mythology, Nian is a beast that attacks people. Each spring

Question

According to Chinese mythology, Nian is a beast that attacks people. Each spring or around the Chinese New Year, it will come down from the mountains to attack people, especially children. One day, a child was playing on a playground and suddenly screamed that Nian has come. The villagers rushed to save him but found no signs of Nian. The next day, the child again screamed that Nian has come, villagers came and again found no signs of Nian. On the third day, the child screamed because Nian really came but nobody came to save the child this time.

Your task is to analyze how the villagers’ belief that the child tells the truth about seeing a Nian decreases over time. You should make the following basic assumptions. The probability that villagers believe the child is 80%. A child whom villagers believe will tell a lie 10% of the time. The probability that a child whom villagers do not believe will tell a lie is 50%.

(a) What is the probability that the villagers still believe the child in the story after finding out that he has not told the truth on the first day?

(b) What is the probability that the villagers still believe the child after finding out that also on the second day he has not told the truth about seeing a Nian?

Explanation / Answer

a)

probability that villager believe the child /he has not told the truth on the first day

is equals to 0.80*0.10 / 0.50 = 0.16

b)

Probability that the villagers still believe the child / also on the second day he has not told the truth about seeing a Nian

is eqauls to 0.80 * 0.10 * 0.10 / 0.50 * 0.50 = 0.032

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