When the occurrence of one event has no effect on the probability of the occurrence of another event are the independent B dependent C mutually exclusive equally likely?

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The two events A and B are said to be incompatible if both events do not occur at the same time. For example, consider the throwing of a coin. Let A be the event where the coin rests on the heads and let B be the event where the coin sits on the tails. It follows that, in a single throw of the right coin, events A and B are not the same. Collaborative variations can be shown in the Venn diagram (read Venn Diagrams). This Venn diagram depicts two special events A and B.

It is not possible for events A and B to occur simultaneously

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Independent Events

Events A and B are said to be independent if the chances of B happening are not affected by the occurrence of event A. For example, suppose we throw a coin twice. Let A be the event where the first coin throws the world to the head. In addition, B should be an event where the second coin throws the earth to the heads. Obviously, the effect of the first coin toss does not affect the effect of the second coin toss. See Tree Pictures for this example in detail. The A and B are independent even as follows.

Consider the illustration of the tree shown here. The probability that incident R occurred near the second branch depends on the outcome of the first incident. The events B and R are not independent. Therefore, they are known as dependent events and related opportunities are conditional.

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What are Mutually Exclusive Events?

Get ready to know the difference between Mutually exclusive and independent events and also to know what mutually exclusive and independent events are!

• Two events let’s suppose event A and event B are said to be mutually exclusive if it is not possible that both of the events (A and B) occur at the same time.

•  For example, let’s consider the toss of a coin. When we toss a coin let A be the event that the coin lands on heads and let B be the event that the coin lands on tails. 

• In a single fair coin toss, events A and B are mutually exclusive which means the outcome can be either tails or heads.  We cannot get both heads and tails at the same time.

•  Mutually exclusive events can be represented using a Venn diagram.

The following Venn diagram given below shows two mutually exclusive events A and B:

If event A occurs, then there is no possibility of the occurrence of event B.

Examples of Mutually Exclusive Events:

There are 52 Cards in a deck:

• the probability of getting a King = 1/13, so we can say P(King)=1/13

• the probability of getting a Queen is = 1/13, so we can say P(Queen)=1/13

 When we combine those two Events, we cannot get queen and king at the same time thus,

 P (A and B ) = 0

Therefore, we can say the probability of a King OR a Queen is (1/13) + (1/13) = 2/13

What are Independent Events?

• Events A and B are known as independent events if the probability of B occurring is unaffected by the occurrence of the event A happening

• For example, let’s suppose that we are tossing a coin twice. Let A be the event that the first coin toss lands on heads and let B be the event that the second coin toss lands on heads.

•  Here, the Occurrence of event A does not affect event B in any manner.

• Independent events can be represented using a Venn diagram.

The following Venn diagram given below shows two independent events A and B:

Formulas of Mutually Exclusive Events and Independent Events!

1. Probability of any event = Number of favorable outcomes / Total number of outcomes

2. For mutually exclusive events  = P(A or B) which can also be written as P(A∪B)

= P(A)+P(B)

And here P(A and B ) = 0

1. For independent events = P(A∩ B) = P(A). P(B)

Difference Between Mutually Exclusive and Independent Event:

At first the definitions of mutually exclusive events and independent events may sound similar to you. The biggest difference between the two types of events is that mutually exclusive basically means that if one event happens, then the other events cannot happen.

Mutually Exclusive and Independent Events

On the other hand, if the events are independent, then it means the occurrence and the outcome of any one event won’t have any effect on the occurrence and outcome of the other events.

Mutually Exclusive vs Independent Events Examples

• Outcomes of rolling a die are mutually exclusive events. You can get either 5 or 6, but you can never get 5 and 6 at the same time. 

• Outcomes of rolling a die two times are independent events. The number we get on the first roll on the die has no effect on the number we’ll get when we roll the die one more time. 

Mutually exclusive and independent events can be differentiated on the basis of Definition, Dependency,  Occurrence of both events, and Venn Diagrams.

Difference Between Mutually Exclusive Event and Independent Event

The following are the key distinctions between mutually exclusive and independent events:

• Mutually exclusive events occur when two or more things happen at the same time. Independent events occur when the occurrence of one event has no bearing on the occurrence of another.

• The occurrence of one event will result in the non-occurrence of the other in mutually exclusive events. In independent events, on the other hand, the occurrence of one event has no bearing on the occurrence of the other.

• P(A and B) = 0 represents mutually exclusive events, while P (A and B) = P(A) P(A)

• The sets in a Venn diagram do not overlap each other in the case of mutually exclusive events, but they do overlap in the case of independent events.

Questions to Be Solved:

Question 1. If we throw a dice twice, then find the probability of getting two 5’s.

Solution Let’s find the probability of getting 5’s,

The formula for finding the probability is,

Probability=Favorable outcomes/Total possible outcomes.

Total possible outcomes when we throw a dice are 6.

Probability of getting 5 on the first throw = 1/6

Probability of getting 5 on the second throw is also = 1/6

Let’s find the probability (Getting two 5’s), since they are independent events,

Formula: P(A∩B) = P(A). P(B)

Probability of getting two 5’s = 1/6 ×1/6

Therefore, Probability of getting two 5’s = 1/6 ×1/6 = 1/36

When the occurrence of one event has no effect on the probability of the occurrence of another event the events are called independent?

When the occurrence of one event has effect on the probability of the occurrence of another event the events are called?

When the occurrence of one has no effect on the occurrence of the other?

When two events are the occurrence of one does not affect the probability of the other occurring?