1.2.6 Example In a quiz show a random integer r between 1 and 10 is generated. A
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Question
1.2.6 Example In a quiz show a random integer r between 1 and 10 is generated. Another, independent such random number s will then be generated, but before that happens, you are invited to guess whether s will be greater than or less than r. If you are correct, then you win s pounds. If you lose (or if s = r) then you win nothing.(i) In the “quiz show” example in the notes (§1.2.6 but reproduced also below), at what value of r does it change from being correct to bet on s being less than r rather than greater?
Explanation / Answer
Solution.
A random Variable is generated R is generated between 1 to 10
Another random variable Number S is also generated
but before it
The contestant is asked weather the next number is greater than R or not .
the above function can be discribed as following
(Being S=R is also case of Failure )
if R is 1 than there are (1 to 10 ) or 10 Cases of S being equal or More than R P = 10/10
If R is 2 than there are (2 to 10 ) or 9 Cases of S being equal or More than R P = 9/10
So the ideal situation for S being Less than R is for 6 and Above numbers
This can be explained with the following Table
.
R Range When contestant shall lose Number of Failures Probability 1 1-10 10 100% 2 2-10 9 90% 3 3-10 8 80% 4 4-10 7 70% 5 5-10 6 60% 6 6-10 5 50% 7 7-10 4 40% 8 8-10 3 30% 9 9-10 2 20% 10 10-10 1 10%Related Questions
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