Conditional Probability

I still don't understand with the given solution on this problem .

Phil is still a compulsive liar who always has a 75% probability of lying. However, we know that he is aware of the winning number in a lottery that consists of choosing a single integer from 1 to a million. He says the winning number is 123. If you were to enter the lottery, which number should you pick to maximize the probability of winning? Make the assumption that if Phil decides to lie about the winning number, he will pick any incorrect (but possible) number with equal probability.

Can somebody explain to me how to solve this?

#Combinatorics

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

It might help if you mentioned a specific question about the solution as to what you don't understand. (It also would help to specify exactly where the problem is. It's in Probability / Conditional Probability / Problem #5) But in any case.

You have a 25% chance of him telling the truth, in which case 123 is correct.

If he isn't then you have a million (well, a million minus 1) possibilities distributed amount the remaining 75%. Let's suppose the real winner is 1. Then you have a .75 * (1/999999) chance of hitting it if you guess. That's a probability of 0.000075% of being right which is a lot worse than 25%!

Note it's generally more efficient to file a report to the specific problem. (Click the three dots marked "more", and pick "report problem".)

Jason Dyer Staff - 3 years, 6 months ago

thank you very much

Frenico Hansen - 3 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$