LECTURE 6 Flashcards
What is probability?
The likelihood of an event occurring, based on past experiences or logical deductions.
What are the possible values of probability?
Probability ranges from 0 (impossible) to 1 (certain).
What does probability of 0 mean?
It represents an impossible event.
What does probability of 1 mean?
It represents a certain event.
What is a trial in probability?
Performing an experiment, such as sowing seeds.
What is an event in probability?
An outcome of an experiment.
What is the sample space (S)?
The set of all possible outcomes in an experiment.
What is a sample point?
An individual element in the sample space.
Give an example of a sample space.
For 5 seeds sown, sample space: {0, 1, 2, 3, 4, 5}.
What are exhaustive events?
The total number of possible outcomes in a trial.
Give an example of exhaustive events.
Throwing a die → Exhaustive events: {1, 2, 3, 4, 5, 6}.
What are favourable events?
Outcomes that satisfy the condition of interest.
Give an example of a favourable event.
For seed germination, germination is a favourable event if we are interested in it.
What are mutually exclusive events?
Events that cannot occur simultaneously.
Give an example of mutually exclusive events.
Seed germination and non-germination.
What are equally likely events?
Events with equal chances of occurrence.
Give an example of equally likely events.
Rolling a die → Each face has an equal chance.
What are independent events?
Events where the occurrence of one does not affect the occurrence of another.
Give an example of independent events.
Germination of one seed does not affect another.
What are dependent events?
Events where the occurrence of one depends on another.
Give an example of dependent events.
Drawing a card without replacement affects the next draw.
What is the formula for classical probability?
P(A) = m/n, where m = favourable cases, n = exhaustive cases.
What is empirical probability?
Probability based on observed data: P(A) = (Number of times A occurs) / (Total trials).
What are the axioms of probability?
- Probability ranges from 0 to 1. 2. Probability of the entire sample space is 1. 3. For mutually exclusive events, P(A ∪ B) = P(A) + P(B).
What is the addition theorem of probability for non-mutually exclusive events?
P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
What is the addition theorem of probability for mutually exclusive events?
P(A ∪ B) = P(A) + P(B).
What is the multiplication theorem for dependent events?
P(A ∩ B) = P(A) × P(B|A).
What is the multiplication theorem for independent events?
P(A ∩ B) = P(A) × P(B).
What is conditional probability?
The probability of event A occurring, given that event B has occurred.
What is the formula for conditional probability?
P(A|B) = P(A ∩ B) / P(B).
What is the probability of getting a sum of 6 when two dice are tossed?
Favourable cases: 5, Total cases: 36, P = 5/36.
What is the probability of getting a sum of 9 when two dice are tossed?
Favourable cases: 4, Total cases: 36, P = 4/36.
What is the probability of drawing a king from a deck of cards?
Favourable cases: 4, Total cases: 52, P = 4/52.
What is the probability of drawing a spade from a deck of cards?
Favourable cases: 13, Total cases: 52, P = 13/52.
What is the probability of drawing a red card from a deck of cards?
Favourable cases: 26, Total cases: 52, P = 26/52.
What is the probability of drawing a numbered card from a deck of cards?
Favourable cases: 36, Total cases: 52, P = 36/52.
What is the probability of 53 Sundays in a randomly chosen leap year?
Favourable cases: 2, Total cases: 7, P = 2/7.
What is the probability of a sure event?
1
Probability can be expressed as which formats?
Ratio, percentage, or proportion.
What is the probability range for any event?
0 to 1.
If A and B are mutually exclusive, what is P(A ∪ B)?
P(A) + P(B).
An integer chosen from 1 to 20 is divisible by 4. What is the probability?
1/4.
Is the mean of a binomial distribution equal to npq?
False.
Define an independent event.
An event unaffected by the occurrence of another event.
State the addition law of probability.
For mutually exclusive events: P(A ∪ B) = P(A) + P(B). For non-mutually exclusive events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
State the multiplication law of probability.
For dependent events: P(A ∩ B) = P(A) × P(B|A). For independent events: P(A ∩ B) = P(A) × P(B).
