Pick the Right Number
To win, the number you picked has to be closer to the drawn number than your friend's pick.
What is the number?
The answer is 36.
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2 solutions
How Albert's probability is 1/3?
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the correct answer should be 36 25 is equally far apart from 15 and 35 which will result in error.
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I believe that you are correct. If 25 was picked then their numbers will be equidistant from it. The correct answer should be 36. I can't find a way to edit the answer.
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There should be a little "pencil" link in the upper right corner of your solution. Clicking that will allow you to edit.
Does the picture have anything to do with the question? For some reason I thought that the number had to be on the bingo card in order for them to win
Slightly different solution attempt, but broadly the same logic.
We realise that if we pick a number below 15, then Albert will have a much larger chance of winning. Therefore, our number, x > 1 5 .
If x > 1 5 , then Bob will the first 15 numbers, as well as half the numbers between x and 15.
This can be expressed as 1 5 + 2 x − 1 5 + 1 .
Meanwhile, I will win on all the numbers between 75 and x , as well as half the numbers between 75 and x .
This can be expressed as ( 7 5 − x + 1 ) + 2 x − 1 5 + 1 .
From this we can form an equation:
( 7 5 − x + 1 ) + 2 x − 1 5 + 1 = 2 ( 1 5 + 2 x − 1 5 + 1 )
7 6 − x + 0 . 5 x − 8 = 3 0 + x − 1 6
− x − x + 0 . 5 x = 8 − 7 6 + 3 0 − 1 6
− 1 . 5 x = − 5 4
x = 3 6
Bob's probability is 2/3 to be twice Albert's of 1/3. Therefore he has to have 50 winning numbers as opposed to Albert's 25.
Albert's winners have to be from 1-25. Bob's from 26-75.
Albert's numbers includes 10 numbers above his 15 therefore Bob's pick should be the 10th number greater starting at 26, which is 35.