IT1807 Sample Space, Relationships Among Events, and Rules of Probability Examples

What does probability describe?

Certainties of events
Past experiences of events
Guarantees of events
Randomness of events (correct)

What is theoretical or classical probability based on?

Random guesswork
Personal bias
Past experience and judgment (correct)
Objective calculations

How are subjective probabilities determined?

Through formal calculations
Based on past experiences (correct)
By flipping a coin
By ignoring personal bias

How does probability differ from guarantees?

Probability involves randomness, guarantees involve certainties (B) Signup and view all the answers

What characterizes subjective probabilities?

They are based on past experience and judgment (A) Signup and view all the answers

How can opinion polls be helpful in determining subjective probabilities?

By aiding in assessing likelihood based on public opinions (C) Signup and view all the answers

How many positions are available for placing the 3 leftmost books on the shelf?

3 (D) Signup and view all the answers

What is the total number of positions available for placing the other 2 books?

2 (B) Signup and view all the answers

How many total positions are there for placing all 5 books?

5 (A) Signup and view all the answers

What is a combination?

A way to select objects without considering order (B) Signup and view all the answers

How many possible combinations exist for placing the English, Spanish, and Algebra books to the leftmost part of the shelf followed by the other 2 books?

12 (C) Signup and view all the answers

In a combination, what does it mean that each object can be selected only once?

Each object can only be chosen once (A) Signup and view all the answers

How is the multiplication principle of counting applied in the context of selecting lunches?

By multiplying the number of main entrées, fruits, and drinks. (B) Signup and view all the answers

Why does the multiplication principle only work when all choices are independent?

Because dependent choices impact the total number of outcomes. (A) Signup and view all the answers

What is the correct formula used to calculate the total number of possible meals?

$3 \times 4 \times 2$ (A) Signup and view all the answers

What happens if one choice in selecting a lunch depends on another choice?

The multiplication principle cannot be used accurately. (D) Signup and view all the answers

Which factor determines the total number of drinks that can be selected for a lunch?

Number of choices for drinks (D) Signup and view all the answers

If there were five main entrées and three drink options instead, how many total meals would be possible?

$5 \times 4 \times 2$ (B) Signup and view all the answers

In the context of the given text, what does the 'multiplication principle of counting' refer to?

Multiplying the number of outcomes for each step (A) Signup and view all the answers

What does 'n' represent in the combination formula discussed?

Size of the full set (A) Signup and view all the answers

What is the purpose of using a combination in selecting two singers for the duet?

To ignore the order of selection (B) Signup and view all the answers

How many singers are auditioning for the musical?

20 (D) Signup and view all the answers

Which aspect of the selection process does 'r = 2' represent?

Number of selected singers (D) Signup and view all the answers

What is the probability that Kevin and Phoebe are selected as the two singers for the duet?

$\frac{1}{190}$ (C) Signup and view all the answers

What is the addition rule for probabilities?

Adding the probabilities of mutually exclusive events (B) Signup and view all the answers

In probability, what do we call events that have no impact on each other?

Independent events (C) Signup and view all the answers

What is Ferguson Probability related to?

Bayesian statistics (B) Signup and view all the answers

How is empirical probability calculated?

By conducting experiments and observing outcomes (D) Signup and view all the answers

What is the key difference between empirical and theoretical probability?

Empirical probability is based on real data, while theoretical probability is based on assumptions. (D) Signup and view all the answers

What formula is used to calculate the probability of independent events occurring together?

$P(A \cap B) = P(A) \times P(B)$ (C) Signup and view all the answers