Question

If a pair of dice is tossed six times what is the probability of getting a total 9 ?

how to solve this on excel?

Answer 1

If a pair of dice is tossed, the probability of getting a total of 9 is, let this event be A:

P(A) = 4/36 [(6,3), (3,6), (5,4), (4,5)]

= 1/9

= p = probability of success

Now the pair is thrown 6 times i.e n = 6 and the probability of getting a total of 9 on each throw is 1/9 i.e. it becomes a binomial distribution with n = 6 and p = 1/9.

So, the probability distribution of a random variable X which denotes the no. of getting a total of 9 on throwing two pair of dice 6 times is as follows:

P(X = x) = nCx*(1/9)^x*(8/9)^n-x

Let's say x = 1

P(X=1) = 0.37

Binomial distribution in Excel:

=BINOM.DIST(number_s,trials,probability_s,cumulative)

The BINOM.DIST uses the following arguments:

1. Number_s (required argument) – This is the number of successes in trials i.e. x
2. Trials (required argument) – This is the number of independent trials. It must be greater than or equal to 0. i.e. n
3. Probability_s (required argument) – This is the probability of success in each trial. i.e. p
4. Cumulative (required argument) – This is a logical value that determines the form of the function. It can either be:
   1. TRUE – Uses the cumulative distribution function. (during inequality sign in x)
   2. FALSE – Uses the probability mass function. (during equality sign in x)

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