when two events are dependent, then p(a and b) = p(a) + p(b). true or false course hero

When are two events a and Bare said to be dependent?

Two events Aand Bare said to be dependent if and only if a) P(A) = P(B) b) P(A) increases along with P(B c) P(A) increases as P(B) decreases. d) event A is affected or changed by the occurrence of event) B

How to find the probability of two dependent events occurring simultaneously?

To find the probability of two dependent events occurring simultaneously, conditional probability is used. If one is altered, it will definitely affect the probability of the other event. The probability of an event given that another event has occurred is termed as conditional probability.

What is a dependent event in psychology?

Dependent events are those events that are affected by the outcomes of events that had already occurred previously. i.e. Two or more events that depend on one another are known as dependent events. If one event is by chance changed, then another is likely to differ.

Are events a and B independent of each other?

Question 1: Let A and B are two independent events such that P (A) = 0.2 and P (B) = 0.8. Find P (A and B), P (A or B), P (B not A), and P (neither A nor B). Answer : Given P (A) = 0.2 and P (B) = 0.8 and events A and B are independent of each other.

What if two events are independent then?

Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur. If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.

When two events are mutually exclusive P A or B p a p/b True False?

A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B) = 0.

When events A and B are independent then?

Events A and B are independent if: knowing whether A occured does not change the probability of B. Mathematically, can say in two equivalent ways: P(B|A) = P(B) P(A and B)

When two events are mutually exclusive What is P A and B?

If two events are mutually exclusive then the probability of both the events occurring at the same time is equal to zero. P(A and B) = 0.

Can dependent events be mutually exclusive?

Dependent events are not necessarily mutually exclusive; they can share sample points while influencing each other's probabilities in other ways.

What is dependent event?

Dependent events are those which depend upon what happened before. These events are affected by the outcomes that had already occurred previously. i.e. Two or more events that depend on one another are known as dependent events. If one event is by chance changed, then another is likely to differ.

What is dependent event probability?

Dependent events: Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs. P(XandY)=P(X)⋅P(Yafterx)

What are dependent and independent events?

Dependent events influence the probability of other events – or their probability of occurring is affected by other events. Independent events do not affect one another and do not increase or decrease the probability of another event happening.

What are examples of dependent events?

Simple examples of dependent events:Robbing a bank and going to jail.Not paying your power bill on time and having your power cut off.Boarding a plane first and finding a good seat.Parking illegally and getting a parking ticket. ... Buying ten lottery tickets and winning the lottery.More items...

Can any two events be both independent and mutually exclusive?

For example: when tossing two coins, the result of one flip does not affect the result of the other. This of course means mutually exclusive events are not independent, and independent events cannot be mutually exclusive.

Can two independent events also be mutually exclusive?

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Which of the two events are mutually exclusive?

Two events are mutually exclusive if they cannot occur at the same time. Another word that means mutually exclusive is disjoint. If two events are disjoint, then the probability of them both occurring at the same time is 0.

What is dependent on whether one event occurs?

Thus, If whether one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.

What is it called when two events depend on one another?

Two or more events that depend on one another are known as dependent events. If one event is by chance changed, then another is likely to differ. Thus, If whether one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.

What is an independent event?

Independent events are those events whose occurrence is not dependent on any other event. If the probability of occurrence of an event A is not affected by the occurrence of another event B, then A and B are said to be independent events.

What is conditional probability of B such that A has already occurred?

If the probability of events A and B are P (A) and P (B) respectively then the conditional probability of B such that A has already occurred is P (A/B).

Why is probability important?

Probability theory is an important topic for those who study mathematics in higher classes. For example, Weather forecast of some areas says that there is a fifty percent probability that it will rain today. The probability is a chance of some event to happen. The term “event” actually means one or more outcomes.

What is probability in science?

The probability is a chance of some event to happen. The term “event” actually means one or more outcomes. The event means the outcome which is able to occur. Total events are defined as all the outcomes which may occur relevant to the experiment asked in the question.

What is the numerator of a simple event?

In the case of a simple event, the numerator (number of favorable outcomes) will be 1.

What is dependent event?

Events are dependent if the outcome of one event affects the outcome of another. For example, if you draw two colored balls from a bag and the first ball is not replaced before you draw the second ball then the outcome of the second draw will be affected by the outcome of the first draw.

How to find the probability of two events?

The probability of two events is dependent if what happens in the first event does affect the probability the second event. P (A + B) = P (A) &times P (B after A)

What is the probability of A and B happening?

If A and B are dependent events, then the probability of A happening AND the probability of B happening, given A, is P (A) × P (B after A).

What is the conditional probability of an event that is independent of another event?

Statistically, An event A is said to be independent of another event B, if the conditional probability of A given B, i.e, P (A | B) is equal to the unconditional probability of A. P (B) ≠ 0.

When do we say two events are independent?

For instance, two independent events will be when you are rolling a dice and flipping a coin.

What is the multiplication rule for independent events?

Answer: The multiplication rule for independent events is said to relate the probabilities of two events to the probability that they both happen. In order to make use of the rule, you need to be having the probabilities of each of the independent events.

What happens if you draw two cards from a pack of cards?

Suppose if we draw two cards from a pack of cards one after the other. The results of the two draws are independent if the cards are drawn with replacement i.e., the first card is put back into the pack before the second draw. If the cards are not replaced then the events of drawing the cards are not independent.

What is the meaning of independent events?

Independent Event. The literal meaning of Independent Events is the events which occur freely of each other. The events are independent of each other. In other words, the occurrence of one event does not affect the occurrence of the other. The probability of occurring of the two events are independent of each other.

What is the value of P (neither A nor B)?

And P (neither A nor B) = P (A’ ∩ B’) = 1 – P (A ∪ B) = 1 – 0.84 = 0.16.

Is B independent of A?

So B is also independent of A.

What is the property of probability where the occurrence of one event does not change the likelihood of another event occurring?

In other words, if the occurrence of one event gives no information about another event, then the two events are independent. (ie. If P (A/B)=P (A), then A and B are independent).

What happens to the probability of outcome A occurring in independence?

For Independence, the probability of outcome A occurring stays the same no matter which outcome of B has occurred.

What is independence in probability?

What is Independence? A property of probability where the occurrence of one event does not change the likelihood of another event occurring. In other words, if the occurrence of one event gives no information about another event, then the two events are independent. (ie. If P(A/B)=P(A), then A and B are independent).