# Calculate Discrete Probability in Excel In this article, we will learn to Calculate Discrete Probability in Excel.

Scenario:

We now define the concept of probability distributions for discrete random variables, i.e. random variables that take a discrete set of values. Such random variables generally take a finite set of values (heads or tails, people who live in London, scores on an IQ test), but they can also include random variables that take a countable set of values (0, 1, 2, 3, …).

Probability means the probable chances of the event occurring in a situation. For example probability of occurring head in tossing of coin which is half (½) as there are two possible outcomes head or tail. Like the probability of raining on a cloudy day is much higher than raining on a clear day. Probability gives us the idea of the occurrence of that event. The mathematical formulation to calculate probability is given by :

Probability = Favourable outcome / total outcome

You can also relate the probability for occuring the rolling of dice or occurrence of getting king in a deck of regular cards. These are the basic probability values which can be calculated manually or by simple mathematical formulation but PROB function helps you find probability for the range of occurrences having discrete probabilities for the event. Let's understand how to use the PROB function.

PROBABILITY formula in Excel

PROB function returns the probability for an event or range of events providing lower and upper limit of an event. X_range and prob_range are different events and their probabilities.

PROB Function syntax:

 =PROB(x_range, prob_range, lower_limit, [upper_limit])

x_range : different events given as array

prob_range : different respective probabilities given as array

lower_limit : probability of an event or lower limit of an event

upper_limit : [optional] only needed when range is given as argument

Example :

All of these might be confusing to understand. Let's understand how to use the function using an example. First we will learn the manual way of calculating probability. Here first we take the example of rolling a regular to dice having 1 to 6  numbers. There are equal chances of getting each number in a roll. So the probability of getting one equal to

Use the formula:

 =1/6 The same will be the probability for each number. So copy the formula using the Ctrl + D or dragging down the C4 cell. Now we want to know the probability of getting 1 or 2 or 3 on rolling the same die. We use the PROB function

Use the formula:

 =PROB(B4:B9, C4:C9, 1, 3)

Explanation :

• B4:B9 is the event range
• C4:C9 is the respective probabilities
• 1 the lower limit of event
• 3 upper limit of the event As you can see the formula returns 0.5 i.e. there are half the chances of getting 1 or 2 or 3 in a roll a dice.

Now let's extend this example for the roll of two dice and we need to calculate the probability of the sum of numbers occurring on the roll. Here we java a table for the Sum on roll of two dice. Now we know the lowest sum we can get is 2 and the highest sum is 12. We use the COUNTIF function to calculate the individual probabilities. Here the sum of getting a number is given as named range data (C3:H8)

Use the formula to count the number of 2s in the data

Use the formula:

 =COUNTIF(data,C11)/COUNT(data) As you can see, using the simple mathematical formula we calculate the probability of getting sum 2 on rolling two dice. Now copy the formula to other cells using the Ctrl + D shortcut or dragging down D11 cell. As you can see we got all the individual probabilities. This will be used as prob)range for the prob function. You must have heard of the game called lucky Seven where person betting can bet on the sum of numbers on rolling two die, there are three events which are less than 7, 7 or greater than 7. In this a person bets on either sum is less than 7 or greater than 7, he gets his bet amount but he bets on exact sum 7 he gets triple the bet amount. Why does this happen? Let's understand this with probability.

Use the formula to get the probability of getting a sum less than 7.

 =PROB(C11:C21, D11:D21, 2, 6)

Explanation :

• C11:C21 is the event range
• D11:D21 is the respective probabilities
• 2 the lower limit of event
• 6 upper limit of the event (less than 7) As you can see, there is 0.42 or 42 percent chance of this happening. Now calculate the getting exact 7.

Use the formula:

 =PROB(C11:C21, D11:D21, 7) As you can see, there are 0.17 or 17 % chances of this event happening. Now calculate the last event happening which is greater than 7.

Use the formula to get the probability of getting a sum greater than 7.

 =PROB(C11:C21, D11:D21, 8, 12)

Explanation :

• C11:C21 is the event range
• D11:D21 is the respective probabilities
• 8 the lower limit of event (greater than 7)
• 12 upper limit of the event As you can see the formula returns 0.42 or 42%. So you can clearly see the difference of probability between the three events.

Here are all the observational notes using the formula in Excel
Notes :

1. The function only works with numbers
2. The function returns #NUM! Error if
1. Any probability value in prob_range is < 0 or > 1.
2. If the sum of all probability in prob_range is not equal to 1.
3. If any of the cell in the x_range or prob_range is blank.
3. The function returns #VALUE! Error if any any value is non-numeric
4. The function returns #N/A error if the supplied x_range and prob_range arrays are of different lengths (i.e. contain different numbers of data points).

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