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Q: Two dice are rolled find the probability that the sum of observed values is equal to 13?

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Yes.

The probability to get a 12, with two dice, is 1/36.

Probability values are never negative and are always between 0-1 according to the definition Probability of A= Number of outcomes classified as A/Total number of possible outcomes

If two fair dice were rolled, there would be 36 outcomes. (1,1),(1,2),....,(6,6) The maximum sum would be 12. Therefore, the probability that the total number of spots shown is equal to 15 is zero.

In statistics, a likelihood function (often simply likelihood) is a function of a statistical model. The likelihood of a set parameter values, given outcomes x, is equal to the probability of those observed outcome.

Since all numbers on a die are 6 or below, the probability is 6/6, 1, or 100%.

The cumulative frequency or the probability of an observed value being less than or equal to a given value. By extension, it would also give the probability of a greater value being observed.

It is the sum of the observed values divided by the number of observations. Each observed value is given equal weight or treated with the same degree of importance.

The chi-squared test is used to compare the observed results with the expected results. If expected and observed values are equal then chi-squared will be equal to zero. If chi-squared is equal to zero or very small, then the expected and observed values are close. Calculating the chi-squared value allows one to determine if there is a statistical significance between the observed and expected values. The formula for chi-squared is: X^2 = sum((observed - expected)^2 / expected) Using the degrees of freedom, use a table to determine the critical value. If X^2 > critical value, then there is a statistically significant difference between the observed and expected values. If X^2 < critical value, there there is no statistically significant difference between the observed and expected values.

For a discrete variable, you add together the probabilities of all values of the random variable less than or equal to the specified number. For a continuous variable it the integral of the probability distribution function up to the specified value. Often these values may be calculated or tabulated as cumulative probability distributions.

From a probability perspective fair means equal probability.

One is the probability, or certain to occur.

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