Fool's problems of the day,

Two very easy problems on probability,

$1.$ Hermoine and Ron decide to check if Harry is under a dark spell. They used the the secrecy sensor to check and realized that he indeed is under it. The probability of the secrecy sensors to read dark spell if the person is under it, is $\frac 9 {10} $. But, Hermoine tells Ron that according the book "Wizarding History", only one in a thousand gets affected by this spell.What is the probability that Harry is actually under the spell?

$2.$ Probability of giving right answer by a student is $\frac 13 $. If eight questions are asked to a student one after the other, what is the probability that a student gives at least two right answer?

Good luck and Enjoy!

Question

Fool's problems of the day,

Two very easy problems on probability,

$1.$ Hermoine and Ron decide to check if Harry is under a dark spell. They used the the secrecy sensor to check and realized that he indeed is under it. The probability of the secrecy sensors to read dark spell if the person is under it, is $\frac 9 {10} $. But, Hermoine tells Ron that according the book "Wizarding History", only one in a thousand gets affected by this spell.What is the probability that Harry is actually under the spell?

$2.$ Probability of giving right answer by a student is $\frac 13 $. If eight questions are asked to a student one after the other, what is the probability that a student gives at least two right answer?

Good luck and Enjoy!

anonymous · Answer

Simple application of Bayes' Theorem for problem one. Problem two take the complement of the probability of the student getting 0 right answers or 1 right answer. I won't put answers for either so people can try them out :)