Enter the number of favorable outcomes and total number of outcomes, as well as the number of trials into the calculator to determine the probability with replacement. This calculator can also evaluate any of the variables given the others are known.

Probability With Replacement Formula

The following formula is used to calculate the probability with replacement. 

P = (n/N)^r

Variables:

  • P is the probability of an event occurring
  • n is the number of favorable outcomes
  • N is the total number of outcomes
  • r is the number of trials

To calculate the probability with replacement, divide the number of favorable outcomes by the total number of outcomes. Raise this quotient to the power of the number of trials. The result is the probability of the event occurring.

What is a Probability With Replacement?

Probability with replacement refers to a statistical event where an item is drawn from a set and then returned to the set before the next draw. This means that the probability of drawing any particular item remains constant for each draw, as the total number of items does not change. This concept is commonly used in scenarios such as drawing cards from a deck, picking balls from a bag, or selecting a number from a set of numbers.

How to Calculate Probability With Replacement?

The following steps outline how to calculate the Probability With Replacement.

  1. First, determine the number of favorable outcomes (n).
  2. Next, determine the total number of outcomes (N).
  3. Next, determine the number of trials (r).
  4. Next, gather the formula from above = P = (n/N)^r.
  5. Finally, calculate the Probability With Replacement.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

number of favorable outcomes (n) = 3

total number of outcomes (N) = 10

number of trials (r) = 2