Not-so-blood sport

Number Theory Level 2

In the movie "Bloodsport", the following bit of dialogue occurs.

FRANK DUX: We could settle this another way. Do you gamble?

SADIO HOSSEIN: What is bet?

Let us assume that "bet" is as follows: Dux proposes that Hossein roll a fair six-sided die, with numbers 1 through 6 on the faces, 4 times. If Hossein rolls a 6 on any of the four rolls, Dux wins the bet. Otherwise, Hossein wins the bet. It is to be made at even odds.

Should Hossein accept the bet?

It doesn't matter: both men have exactly a 50% chance to win No Yes Not enough information given to determine the answer

Denton Young by Denton Young , 47, USA

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2 solutions

All it takes is for Hossein to throw a 6 on any of the 4 chances he was given. This means he could win by the first, second, third of fourth throw. Mathematically, pr(6)= 1/6+(5/6x 1/6)+(5/6 x 5/6 x 1/6)+(5/6 x 5/6 x 5/6 x 1/6)=671/1296 And this is more than 50%. Hence Hosseim should bet. I answered wrongly hahahah

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Denton Young
Feb 11, 2017

The chance of Hossein not throwing a 6 on any given roll is 5/6.

So the chances that he does not throw a 6, 4 times in a row, is ( 5 / 6 ) 4 (5/6)^4 = 625/1296, which is less than 50%.

So, at even odds, he should not accept the bet.

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If the odds of not throwing a six is less than 50% then the odds of throwing a six would be greater than 50% .

1-(5/6)^4 = 671/1296 = 51.77%

This being the case you would not best. I think there is a flaw in your calculation?

Randy Yap - 4 years, 3 months ago

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I think you meant to reply to P Peh :)

Denton Young - 4 years, 3 months ago

No I meant to you Denton. The question is asking for the probabil out of getting a 6. In four rolls. You answered the question as to the probability of not getting a 6 in four rolls.

Randy Yap - 4 years, 3 months ago

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Actually, the question is asking if it is wise for Hossein to accept the bet. Assume he should only accept it if he has at least a 50% chance of winning it.

Then we need to calculate his chances of winning, which I did. His chances of winning are, as shown in my solution, 625/1296, which is less than 50%.

Therefore, the answer is: No, he should not accept the bet.

Denton Young - 4 years, 3 months ago

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