LECTURE 6

Question 1

What is probability?

Answer 1

The likelihood of an event occurring, based on past experiences or logical deductions.

Question 2

What are the possible values of probability?

Answer 2

Probability ranges from 0 (impossible) to 1 (certain).

Question 3

What does probability of 0 mean?

Answer 3

It represents an impossible event.

Question 4

What does probability of 1 mean?

Answer 4

It represents a certain event.

Question 5

What is a trial in probability?

Answer 5

Performing an experiment, such as sowing seeds.

Question 6

What is an event in probability?

Answer 6

An outcome of an experiment.

Question 7

What is the sample space (S)?

Answer 7

The set of all possible outcomes in an experiment.

Question 8

What is a sample point?

Answer 8

An individual element in the sample space.

Question 9

Give an example of a sample space.

Answer 9

For 5 seeds sown, sample space: {0, 1, 2, 3, 4, 5}.

Question 10

What are exhaustive events?

Answer 10

The total number of possible outcomes in a trial.

Question 11

Give an example of exhaustive events.

Answer 11

Throwing a die → Exhaustive events: {1, 2, 3, 4, 5, 6}.

Question 12

What are favourable events?

Answer 12

Outcomes that satisfy the condition of interest.

Question 13

Give an example of a favourable event.

Answer 13

For seed germination, germination is a favourable event if we are interested in it.

Question 14

What are mutually exclusive events?

Answer 14

Events that cannot occur simultaneously.

Question 15

Give an example of mutually exclusive events.

Answer 15

Seed germination and non-germination.

Question 16

What are equally likely events?

Answer 16

Events with equal chances of occurrence.

Question 17

Give an example of equally likely events.

Answer 17

Rolling a die → Each face has an equal chance.

Question 18

What are independent events?

Answer 18

Events where the occurrence of one does not affect the occurrence of another.

Question 19

Give an example of independent events.

Answer 19

Germination of one seed does not affect another.

Question 20

What are dependent events?

Answer 20

Events where the occurrence of one depends on another.

Question 21

Give an example of dependent events.

Answer 21

Drawing a card without replacement affects the next draw.

Question 22

What is the formula for classical probability?

Answer 22

P(A) = m/n, where m = favourable cases, n = exhaustive cases.

Question 23

What is empirical probability?

Answer 23

Probability based on observed data: P(A) = (Number of times A occurs) / (Total trials).

Question 24

What are the axioms of probability?

Answer 24

1. 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).

Question 25

What is the addition theorem of probability for non-mutually exclusive events?

Answer 25

P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Question 26

What is the addition theorem of probability for mutually exclusive events?

Answer 26

P(A ∪ B) = P(A) + P(B).

Question 27

What is the multiplication theorem for dependent events?

Answer 27

P(A ∩ B) = P(A) × P(B|A).

Question 28

What is the multiplication theorem for independent events?

Answer 28

P(A ∩ B) = P(A) × P(B).

Question 29

What is conditional probability?

Answer 29

The probability of event A occurring, given that event B has occurred.

Question 30

What is the formula for conditional probability?

Answer 30

P(A|B) = P(A ∩ B) / P(B).

Question 31

What is the probability of getting a sum of 6 when two dice are tossed?

Answer 31

Favourable cases: 5, Total cases: 36, P = 5/36.

Question 32

What is the probability of getting a sum of 9 when two dice are tossed?

Answer 32

Favourable cases: 4, Total cases: 36, P = 4/36.

Question 33

What is the probability of drawing a king from a deck of cards?

Answer 33

Favourable cases: 4, Total cases: 52, P = 4/52.

Question 34

What is the probability of drawing a spade from a deck of cards?

Answer 34

Favourable cases: 13, Total cases: 52, P = 13/52.

Question 35

What is the probability of drawing a red card from a deck of cards?

Answer 35

Favourable cases: 26, Total cases: 52, P = 26/52.

Question 36

What is the probability of drawing a numbered card from a deck of cards?

Answer 36

Favourable cases: 36, Total cases: 52, P = 36/52.

Question 37

What is the probability of 53 Sundays in a randomly chosen leap year?

Answer 37

Favourable cases: 2, Total cases: 7, P = 2/7.

Question 38

What is the probability of a sure event?

Answer 38

1

Question 39

Probability can be expressed as which formats?

Answer 39

Ratio, percentage, or proportion.

Question 40

What is the probability range for any event?

Answer 40

0 to 1.

Question 41

If A and B are mutually exclusive, what is P(A ∪ B)?

Answer 41

P(A) + P(B).

Question 42

An integer chosen from 1 to 20 is divisible by 4. What is the probability?

Answer 42

1/4.

Question 43

Is the mean of a binomial distribution equal to npq?

Answer 43

False.

Question 44

Define an independent event.

Answer 44

An event unaffected by the occurrence of another event.

Question 45

State the addition law of probability.

Answer 45

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).

Question 46

State the multiplication law of probability.

Answer 46

For dependent events: P(A ∩ B) = P(A) × P(B|A). For independent events: P(A ∩ B) = P(A) × P(B).