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Suppose a die has been loaded so that a six is scored five times more often than any other score, while all the other scores are equally likely. Express your answers to three decimals.

I have gotten the following answers.

What is the probability of scoring a three?

0.090909091 I have deciphered since it is a 11 sided die so I simply came up with 1/11 since there is only 1/11 chance of getting a 3

What is the probability of scoring a six? 0.454545455 I have reasoned since there are 5 chances in the 11 sided die so I have gotten 5/11.

I have gotten both of them wrong. What are the answers?

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    Your probabilities don't add to $1$. You have five faces each with probability $\frac 1{11}$ and one with probability $\frac 5{11}$, hence a total probability of $\frac {10}{11}$. Try working with a ten sided die. – 2017-01-31
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    a way to do this is if x is the probability of a 3, then 5x is the probability of a 6, there are 5 numbers with x as a probability (1,2,3,4,5) , the total of all probabilities is 5x + 5x = 10x and has to equal 1 - so what is x, the probability of a 3? – 2017-01-31
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    Oh what were the answers then? – 2017-01-31

3 Answers 3

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Let $x$ be the probablity of getting a particular nonsix number. So, by question the probablity of getting a six is $5x$.

Since there are 5 nonsix numbers, the probablity of getting a nonsix number is $5x$.

Since the probablity of getting a number is $1$, the probablity of getting a six $5x$, and getting a nonsix also $5x$, so:

$$1=5x+5x$$

Solving which we get:

$$x=0.1$$

So, since the probablity of getting a particular nonsix is $x$, the probablity of getting $3$ is $0.1$.

Similarly, the probablity of getting a $6$ is $5x$, so it is $0.5$

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    This makes sense. Have an amazing day! – 2017-01-31
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    @Mckayla Thanks. – 2017-02-01
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A die with 5 times the probability of rolling a six is the same as a ten sided die with five sixes on it. As the sides are 1, 2, 3, 4, 5, 6, 6, 6, 6, 6.

Probability of rolling a 3 = $\frac 1{10} = 0.1$

Probability of rolling a 6 = $\frac 5{10} = 0.5$

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    If you are downvoting write the reason please. – 2017-01-31
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    Hello thank you for the response. All the best. – 2017-01-31
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Possibly the problem is in the interpretation of 'five times more often than any other score'. It can be read in two ways.

You read it as: 'the probability of getting 6 is 5 times the probability of getting 3'.

The other way of reading it (which is probably intended) is as: 'the probability of getting 6 is 5 times the probability of getting a non-6'.

In your 11 sided die the number of sides which are non-sixes is still pretty high even if only one of them reads 3.

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    What formula and approach should I use instead to solve: What is the probability of scoring a three? What is the probability of scoring a six? – 2017-01-31
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    First: I am not sure that what I write is the correct interpretation of the problem. The comments to your original question above by lulu en Cato explain how to amend your computation if your original interpretation of the question *was* correct after all! – 2017-01-31
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    But when working with the interpretation of my answer: there are different approaches. I actually really liked your idea of modeling the unfair die with a fair die that just has a lot more sides to it. However: to get a die with 5 times as much sixes on it as it has numbers of any other kind you really need to crank up the number of sides way beyond 11. – 2017-01-31
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    Oh I was just wondering what the answers were for both of them. It's hard to understand 4 in the morning with 3 hours of sleep. – 2017-01-31
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    The policy of the website is to only give hints not answers in these kinds of situations. I am sure you will be able to solve the problem with the hints provide here after getting some more sleep. – 2017-01-31