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Dependent Events: Two events can be said to be dependent when the specific outcome of the 1^{st} event actually influences the outcome of the 2^{nd} event. The probability of the 2 dependent events can be said to be the product of the probability of the X and the probability of the Y AFTER X actually occurs. It should be noted that the dependent events in the probability actually mean those events whose occurrence of 1 actually affects the probability of the occurrence of any other. For instance, suppose a bag consist of 3 red as well as 6 green balls. 2 balls can be said to be drawn from bag 1 subsequent to the other. Let A be the event of the drawing of the red ball in the 1^{st} draw and B be the specific event of the drawing of the green ball in the 2^{nd} draw. If the specific ball drawn in the 1^{st} draw is not actually replaced back in the concerned bag, then A and B can be said to be the dependent events as P(B) is increased or decreased in accordance with the 1^{st} draw results as a green or a red ball.

The dependent events in the probability actually mean those events whose occurrence of 1 actually affects the probability of the occurrence of any other. For instance, suppose a bag consist of 3 red as well as 6 green balls. 2 balls can be said to be drawn from bag 1 subsequent to the other. Let A be the event of the drawing of the red ball in the 1^{st} draw and B be the specific event of the drawing of the green ball in the 2^{nd} draw. If the specific ball drawn in the 1^{st} draw is not actually replaced back in the concerned bag, then A and B can be said to be the dependent events as P(B) is increased or decreased in accordance with the 1^{st} draw results as a green or a red ball. Dependent events can be said to be the ones that depend upon what happened or transpired before. These events are actually affected by the outcomes that had already transpired previously. That is, 2 or more events that depend upon 1 another are called to be the dependent events. If 1 event is by chance altered or changed, then any other is likely to differ.

For the events to be considered dependent, 1 should have an influence over the manner in which probable another is. In other terms, a dependent event might only transpire if any other event occurs first. While this can be said to be a mathematic/statistical term, speaking particularly, to the subject of the probabilities, the same can be said to be true of the dependent events as they transpire in the real world. For instance, say one would like to go on a vacation at the concluding time of the next month, but that actually depends upon having enough money to actually cover the trip. One might be counting on any bonus, any commission, or any advance on the paycheck. It also most probably depends upon a person being given the final week of the month off to make the trip. The main focus while analyzing dependent events can be said to be probability. The occurrence of a single event exerts a specific effect upon the probability of any other event. One must consider the following examples: -

- Getting into any traffic accident can be said to be dependent upon driving or riding in any vehicle.
- If one parks the vehicle illegally, the one is more likely to get a parking ticket.
- One should purchase a lottery ticket to have any chance at winning; the odds of winning can be said to be increased if one buys more than a single ticket.
- Committing any serious crime – like breaking into anybody’s house – increases the odds of getting caught as well as going to jail.

Events can be said to be dependent if the specific outcome of a single event affects the specific outcome of any other. For instance, if one draws 2 colored balls from any bag as well as the 1^{st} ball is not replaced prior to when one draws the 2^{nd} ball then the specific outcome of the 2^{nd} draw shall be affected by the specific outcome of the 1^{st} draw.

If A and B can be said to be the dependent events, then the probability of the A happening AND the probability of the B happening, provided A is P(A) × P(B after A).

P(A and B) = P(A) × P(B after A),

P(B after A) can also be written as P(B | A),

Then, P(A and B) = P(A) × P(B | A)

Events can be said to be dependent if the specific outcome of a single event affects the specific outcome of any other. For instance, if one draws 2 colored balls from any bag as well as the 1st ball is not replaced prior to when one draws the 2nd ball then the specific outcome of the 2nd draw shall be affected by the specific outcome of the 1st draw.

Two events can be said to be dependent when the specific outcome of the 1^{st} event actually influences the outcome of the 2^{nd} event. The probability of the 2 dependent events can be said to be the product of the probability of the X and the probability of the Y AFTER X actually occurs.

Simple examples of dependent events: -

- Robbing a bank and going to jail.

Independent events can be said to be those events whose occurrence is not actually dependent on any other event.

For instance, a coin is flipped in the air and the outcome is Head, and again the coin is flipped, but this time outcome is Tail. In two cases, the occurrence of both events is independent of one another.

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