Mathematics Chapter 5: Probability

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Questions and Answers

In the provided hospital data, what is the total count of individuals using private hospitals?

  • 200
  • 90
  • 70 (correct)
  • 110

Using the provided data, what is the risk of depression for females?

  • 0.16
  • 0.14
  • 0.02 (correct)
  • 0.52

What does the additive rule state concerning the probability of mutually exclusive outcomes?

  • The probability of any one of several mutually exclusive outcomes occurring is the sum of their probabilities. (correct)
  • The probability of any one of several mutually exclusive outcomes occurring is the product of their probabilities.
  • The probability of any one of several mutually exclusive outcomes occurring is the square root of their probabilities.
  • The probability of any one of several mutually exclusive outcomes occurring is the difference of their probabilities.

In the hospital data, what proportion of the total group is represented by insured individuals?

<p>0.45 (D)</p> Signup and view all the answers

Considering a bag of 80 M&Ms with 20 of each of the colors red, blue, green, and orange, what is the probability of drawing a red, blue, or orange M&M in a single draw?

<p>0.75 (D)</p> Signup and view all the answers

Based on the provided data, calculate the risk ratio of depression for males compared to females.

<p>7.00 (D)</p> Signup and view all the answers

What is the total number of uninsured individuals across both public and private hospitals?

<p>110 (D)</p> Signup and view all the answers

What defines independent outcomes in probability?

<p>The probability of one outcome does not affect the probability of other outcomes. (D)</p> Signup and view all the answers

What does the multiplicative rule state about the probability of two independent outcomes occurring?

<p>The probability is the product of their individual probabilities. (A)</p> Signup and view all the answers

Using the dinner bag of M&Ms with the same distribution as the lunch bag, what is the probability of drawing a red M&M, replacing it, and then drawing a green M&M?

<p>0.0625 (D)</p> Signup and view all the answers

If two probabilities, both less than 1, are multiplied together, what is the relationship of the product to the value of the individual probabilities?

<p>The product will be less than either of the individual probabilities. (D)</p> Signup and view all the answers

Which of the following best describes complementary outcomes?

<p>Outcomes where the sum of their probabilities equals 1 and only two possible outcomes exist. (C)</p> Signup and view all the answers

What is the key characteristic of conditional probability?

<p>The probability of an outcome changes depending on the occurrence of another outcome. (C)</p> Signup and view all the answers

Using the data provided (Insured (INS) Uninsured (UNI) / Public Hospital (PUB) Private Hospital (PRI)), what is the probability of a mother being uninsured (UNI) and giving birth in a public hospital (PUB)?

<p>0.40 (D)</p> Signup and view all the answers

Which calculation correctly demonstrates the probability of getting heads or tails using a coin?

<p>$P(heads) + P(tails) = .5 + .5 = 1.00$ (D)</p> Signup and view all the answers

When calculating odds, which value is typically placed in the numerator to yield a result greater than one?

<p>The larger frequency of occurrence (D)</p> Signup and view all the answers

What is the definition of 'odds' as presented in the text?

<p>The frequency of one event divided by another (B)</p> Signup and view all the answers

Based on the provided data, what is the approximate odds ratio of being depressed for males compared to females?

<p>8.5 (D)</p> Signup and view all the answers

In meta-analyses with binary outcomes, what is the most common measure of effect size?

<p>Odds ratios (C)</p> Signup and view all the answers

What is a key characteristic of a meta-analysis, as described in the provided content?

<p>It analyzes multiple independent studies to find overall trends. (C)</p> Signup and view all the answers

If the probability of an event is 0.25, what is the most accurate representation of this probability?

<p>1:4 (B)</p> Signup and view all the answers

If the relative frequency of observing a certain outcome is 0.80 what is the probability of observing that outcome?

<p>0.80 (B)</p> Signup and view all the answers

A sample space of an event is defined as:

<p>The total number of potential outcomes for a random event. (A)</p> Signup and view all the answers

Which of these values is NOT a valid probability?

<p>-0.25 (A)</p> Signup and view all the answers

What does it mean for two outcomes to be mutually exclusive?

<p>The two outcomes cannot occur simultaneously. (D)</p> Signup and view all the answers

Which of the following is an example of mutually exclusive outcomes?

<p>Drawing a jack or a queen from a standard deck of cards. (A)</p> Signup and view all the answers

A bag contains 2 oranges and 3 apples. Are the outcomes of drawing an orange or drawing a fruit from the bag mutually exclusive?

<p>No, because drawing an orange is a subset of drawing a fruit. (A)</p> Signup and view all the answers

If the sample space has 8 possible outcomes, and a particular event occurs 2 times, what is the probability of that event, expressed as a simple fraction?

<p>1/4 (B)</p> Signup and view all the answers

Flashcards

Probability

The likelihood of an outcome or event. Calculated as the frequency of the outcome divided by the total number of possibilities.

Sample space

The set of all possible outcomes of an event.

How probabilities are written

Probability can be expressed in different ways, including fractions, decimals, percentages, and proportions.

Range of probabilities

Probabilities always fall between 0 and 1, meaning they can't be negative.

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Mutually exclusive events

Two events that cannot occur together.

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Probability of mutually exclusive events

The probability of event A and event B occurring together is zero.

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Mutually exclusive events (relationship)

The occurrence of one event prevents the occurrence of the other.

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Non-mutually exclusive events

Outcomes that can occur together.

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Additive Rule

The probability of any of several mutually exclusive events happening is calculated by adding their individual probabilities.

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Independent Outcomes

Events that have no impact on each other's probabilities. The outcome of one event does not affect the outcome of another.

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Multiplicative Rule

In independent events, the probability of both events happening together is the product of their individual probabilities.

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Dependent Outcomes

A situation where the probability of an event changes based on the outcome of a previous event.

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Probability Range

Probability values always fall between 0 and 1, where 0 represents an impossible event, and 1 represents a certain event.

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Product of Probabilities

Two probabilities with values less than 1 multiplied together result in a product smaller than either individual probability.

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Complementary Outcomes

Two outcomes that cover the entire sample space. The sum of their probabilities equals 1.

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Conditional Outcomes

The probability of one event happening depends on whether another event has already occurred.

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Conditional Probability

The probability of an event happening given that another event has already occurred. Represented as P(A|B), meaning the probability of A happening given that B has happened.

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Probability of Uninsured Mother in Public Hospital

The probability of selecting an uninsured mother who gave birth in a public hospital.

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Risk (Statistics)

In statistics, risk refers to the probability of an event occurring. It is calculated by dividing the number of occurrences of that event by the total number of possible occurrences.

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Risk Ratio

Ratio of two risks. It's used to compare the likelihood of an event in two different groups.

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Contingency Table

A table that displays the frequency of events in two or more categories. Each cell in the table represents the number of occurrences in the intersection of two categories.

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Exposed Group

A group in which the exposure or intervention of interest is present. The risk of an event is calculated in this group.

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Control Group

A group in which the exposure or intervention of interest is absent. The risk of an event is calculated in this group.

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Odds

The likelihood of an event happening, calculated as the frequency of that event divided by the frequency of another event.

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Odds Ratio

The ratio of two odds, often used to compare the likelihood of an event in two different groups or under different conditions.

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Meta-analysis

A statistical method that combines the results of multiple independent studies to produce a more robust and reliable overall conclusion.

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Odds Ratio in Meta-analyses

A measure used to quantify the effect size of a treatment or factor in studies with binary outcomes (yes/no, success/failure).

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Meta-analysis of Binary Outcomes

A statistical analysis that combines the results of multiple independent studies to determine overall findings, often used in research to assess the effectiveness of interventions or prevalence of conditions.

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Study Notes

Chapter 5: Probability

  • Probability (p) is the likelihood of an outcome or event.
  • It's calculated by: dividing the frequency of an outcome occurring (f(x)) by the total possible outcomes (sample space).
  • Sample space is the number of possible outcomes for a random event.
    • For one coin toss, the sample space is 2 (Heads, Tails).
    • For two coin tosses, the sample space is 4 (HH, HT, TH, TT).

Probabilities Representation

  • Probabilities can be expressed as fractions, decimals, percentages, or proportions.

Probability Constraints

  • Probabilities are always between 0 and 1.
  • Probabilities cannot be negative.

Relationships Between Outcomes

  • Probability calculations depend on how outcomes relate to each other:
    • Mutually exclusive: Two outcomes cannot occur simultaneously (e.g., coin toss - heads or tails).
    • Independent: The probability of one outcome doesn't affect the probability of another (e.g., consecutive coin tosses).
    • Complementary: Two outcomes that constitute the entire sample space, and their probabilities sum to 1 (e.g., coin toss - heads and tails).
    • Conditional: The probability of one outcome depends on another (e.g., drawing an M&M without replacement).

Additive Rule

  • The probability of one of several mutually exclusive outcomes is the sum of their individual probabilities.
    • E.g., Drawing a red or blue M&M from a bag: (probability of red) + (probability of blue).

Multiplicative Rule

  • The probability of two independent outcomes occurring is the product of their individual probabilities.
    • E.g., Probability of drawing a red, then a blue M&M (with replacement): (probability of red) x (probability of blue).

Risk

  • Risk is the number of occurrences of an event divided by the total number of occurrences.

Risk Ratio

  • Risk ratio or Relative risk is the ratio of two risks.
  • Calculated by dividing a risk (e.g., female) by comparable risks (e.g., male)

Odds

  • Odds are the frequency of occurrence of one event divided by the frequency of occurrence of another.

Odds Ratio

  • Odds ratio is the ratio of two odds.

Meta-Analysis

  • A statistical analysis of multiple independent studies, used to determine more precise overall findings.
  • Useful for synthesizing inconsistent results from different studies.

Examples of Findings from Meta-Analyses

  • Psychological interventions may or may not reduce suicidal ideation
  • Tinnitus is associated with psycholigical impairments.

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Chapter 5 Probability PDF

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