# Independent Probability Calculator

**Created By :** Vaibhavi Kumari

**Reviewed By :** Rajashekhar Valipishetty

**Last Updated :** Mar 24, 2023

Free Independent Probability Calculator will find the probability of various independent events and displays the outcome within no time. Give the probability of each independent event as input in the calculator and make your calculations easier & quicker.

### What are Independent Events ?

A probability event can be defined as the set of outcomes of a random experiment. The two types of events in probability are dependent events and independent events.

The two events are said to be independent events when the outcome of the first event does not show an impact on the outcome of the second event. The example is tossing a coin and rolling a die simultaneously or separately are independent. The formulas to calculate the probability of independent events are along the lines:

If two events A, B are independent, then the probability of happening A and B is here:

**P(A ∩ B) = P(A) . P(B)**

For three independent events A, B, C, the probability of happening A, B, C is:

**P(A ∩ B ∩ C) = P(A) . P(B) . P(C)**

So, according to the **multiplication rule** to calculate the probability of the intersection of independent events, multiply the probabilities of each event together.

### Steps to Find the Probability of Independent Events

The method to find the independent events probability is enclosed here. Make use of these guidelines to get immediate results.

- Initially, check whether the given events are independent or not.
- If independent, then multiply the probability of each event with another.
- Finally, obtained produt is the independent probability.

**Example: **In a survey, a company found that 8 out of 15 buy pens. If four people are chosen at random with replacement, what is the probability that all 4 people buy pens?

Solution:

If four people are chosen at random with a replacement who buy pen, then the probability that all 4 people buy pen is:

P(1st person buys pen) = 8/15

P(2nd person buys pen) = 8/15

P(3rd person buys pen) = 8/15

P(4th person buys pen) = 8/15

P(all 4 persons buy pen) = 8/15 x 8/15 x 8/15 x 8/15

= 4096/50625

The probability that all 4 people buy pen is 4096/50625.

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### FAQ's on Independent Events Probability Calculator

**1. What is an independent event in probability?**

Two events are called independent events if the outcome of one event does not affect the outcome of another. The real-time example is scoring marks in the exams, taking a cab to market has no effect on finding listening to your favourite song.

**2. How do you calculate the probability of 3 independent events?**

You need to multiply the probabilities of all three independent events to get the final probability of three events occurring.

**3. What is an example of an independent event?**

One example that defines an independent event is if we toss a coin, and observe the outcome as head, again toss a coin, the outcome is tail. In both situations, the occurrence of both events is independent of each other.

**4. How to know if an event is an independent event?**

Events A and B are said to be independent if the equation P(A∩B) = P(A) . P(B) holds true. You can multiply the probabilities of two events if it is equal to the probability of two events, then they are independent.