What is conditional probability?

Conditional Probability is when an outcome is dependant on the probability of another event happening.

For example, we have the outcome of being late to school or being early to school, however, it is dependent on the probability of oversleeping.

Hello! How's it going? I would describe it as follows..... The conditional probability is the chances of an event or outcome that it itself based on the occurrence of some other previous event or outcome! Hope that helps!

Conditional probability is the probability of one event occurring with a relationship to one or more other events.

For example Conditional probability could describe an event like:

• Event A is that it is snowing outside, and it has a 0.2 (20%) chance of snowing today. 
• Event B is that you will need to go outside, and that has a probability of 0.4 (40%).

A conditional probability would look at these two events in relationship with one another, such as the probability that it is both snowing and you will need to go outside. With probability and means multiply and or means add

so to work this out you would multiply 0.2 by 0.4 to get 0.08.

Conditional probability is:

The probability of event A can change depending on the outcome of a previous event.

For example, the probability of your being late from work may change depending on whether you oversleep or not.

We use conditional probability to model situations when the probability of an event can change depending on the outcome of a previous event. For example, the probability of your being late for work may change depending on whether there was a traffic congestion or not.

The probability that event B occurs given that event A has already occurred is written as p(B|A).

Example:

Given that you drew a red card, in a standard 52-card pack, what is the probability that it's an ace?

p(ace|red) = 2/26 = 1/13. Hence, out of the 26 red cards (given a red card), there are two aces and 2/26 = 1/13.

Hi Maxine

Conditional Probability means when one event occurs, apply one condition over it. Let's take the case of playing cards. In total there are 52 cards - 26 black and 26 red. Now you will have to find the probability of choosing a four out of black cards - which is a condition actually. And there are only 2 four cards in 26 black cards, so p(four| black) = 2/26 = 1/13.

Hope it may help you!

It's the probability of Event A occurring given that B has occurred.

Hence you find the probability of B and A occurring within the probability of B.

conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence). This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditionally probability with respect to A.

Definition

Conditional probability simply means: the chance that B happens, given that A happens. For example, given it is raining, what is the chance I slip over in the mud?

Notation

First, let's go through some common notation we use in probability.

Event: event means an outcome. This can mean anything from pulling a red ball out of a bag, to getting a divorce, to scoring a goal.

P(A): P(A) means the probability that event A happens, written as a decimal. So, if rain is event A and there's a 50% chance of rain, P(A) would be 0.5. And if me slipping over in the mud is event B, and that happens 10% of the time P(B) would be 0.15.

P(A n B): P(A n B) is the probability that event A happens AND event B happens. So, let's imagine say the probability that it rains (event A), AND I slip over in the mud (event B) is one in four, then P(A n B) = 0.1. Note that I've put an 'n' here because I'm on a computer, but the sign in the middle looks more like an upside-down u.

P(A|B): is the probability of event A, given event B happens. In the same way, P(B|A) is the probability of event B, given event A happens. This is conditional probability - it's the probability under the condition that another event happens.

Calculation

Calculating conditional probability is actually very easy once you practice. We just need two bits of information.

Let's return to our original example. Given it is raining, what is the chance I slip over in the mud?

If we say event A is rain, and event B is slipping in the mud, we need to work out P(B|A), the probability of event B given event A happens.

To work this out, we have a formula:

P(B|A)= P(A n B) / P(A)

From our example, we know P(A), the probability of rain, is 0.5. We also know that P(A n B), the probability that it rains and I fall, is 0.1.

Putting this into our formula, we get P(B|A) = 0.1/0.5 = 0.2.

If A and B are two events in a sample space, S, then the conditional probability of A given B happens is:

P(A|B) = P(A ∩ B)

P(B)

assuming the probability of B, denoted as P(B) above, is greater than 0 (i.e. P(B)>0 ).

(Here, the "probability of A given B" is denoted as P(A|B) and the "probability of the intersect of A and B", i.e., the probability that both A and B happen is denoted as P(A ∩ B)

Conditional Probability is also known as dependent Probability which means that one event will occur at the expense of the the other event.