What is the probability of getting at most two heads when three unbiased coins are tossed?

To find the probability of getting at most two heads, we can use the rule of complements by finding the probability of getting three heads and subtracting it from 1.

What are objective probabilities?

Probabilities that can be estimated from long-run proportions (normally via data collection).

1/36

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Rule of Complements

To find the probability of getting at most two heads, we can use the rule of complements by finding the probability of getting three heads and subtracting it from 1.

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Objective Probabilities

Probabilities that can be estimated from long-run proportions (normally via data collection).

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Mutually Exclusive Events

The intersection of events A and B, showing the outcomes that are common to both events.

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First Law of Probability

A number between zero and one.

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Equally Likely Events

Assuming balanced coin when it is tossed, assuming fair die when it is thrown, and assuming tickets are all in exactly the same appearance when they are drawn.

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Equally Likely Events

The probabilities derived theoretically may not be accurate.

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First Law of Probability

It is certain not to occur.

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Event as a Collection of Outcomes

An event is a collection of outcomes.

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Event as a Collection of Outcomes

To visually represent the relationships between different events and their intersections.

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Probability of an Outcome

P(E) = 13/52

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Event as a Collection of Outcomes

At least one of the outcomes must occur when the experiment is performed.

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Space and Experiment Outcomes

The sample space of the experiment.

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Event as a Collection of Outcomes

10.

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Mutually Exclusive Events

No two outcomes can occur together.

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Space and Experiment Outcomes

30.

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Subjective Probabilities

Probabilities that cannot be estimated from long-run proportions and are normally opinions or guesses given by people.

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Objective Probabilities

As a proportion or a percentage.

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First Law of Probability

Greater likelihood.

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Probability of an Outcome

5/6 or 0.8333.

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Rule of Complements

The probability of an event occurring is 1 minus the probability of the event not occurring.

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Event as a Collection of Outcomes

15.

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Mutually Exclusive Events

Events that cannot occur at the same time.

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Second Law of Probability

If A and B are mutually exclusive events, then the probability of either A or B occurring is the sum of the probabilities of A and B.

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Probability of an Outcome

The likelihood that the outcome will occur when the uncertainty is resolved.

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Subjective Probabilities

The probability that Brazil will win the next world cup.

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Objective Probabilities

The proportion of times that the event occurs out of the number of times the random experiment is run.

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Subjective Probabilities

Subjective probabilities.

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Mutually Exclusive Events

The overlap between two events, indicating that they can occur together.

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Space and Experiment Outcomes

An activity that results in one of several possible outcomes.

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Equally Likely Events

Events where outcomes have an equal chance of occurring.

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Equally Likely Events

Tossing a balanced coin or throwing a fair die.

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First Law of Probability

It is virtually certain to occur.

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Event as a Collection of Outcomes

The event of picking a spade.

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Event as a Collection of Outcomes

The event of picking a seven.

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Space and Experiment Outcomes

Two separate circles that do not overlap.

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Probability of an Outcome

P(F) = 4/52

Study Smarter, Not Harder

Study Smarter, Not Harder