Basic Probability 1

Question 1

What are examples of chance?

Answer 1

• the odds of being struck by lightening - 1 in 3 million

- the odds of winning the lottery - 1 in 14 million

Question 2

How is basic probability used in business?

Answer 2

Owner of a corner shop wants to supply newspapers. Must decide how much to buy (Q) from wholesaler at wholesaler price (W). Any unused papers cannot be sold = OC. How many should be bought? Based on previous demand as demand for newspapers realises in the day

Question 3

Which 10 adjectives represent certainty?

Answer 3

1. Certain
2. Expected
3. Likely
4. Probable
5. Not unreasonable that
6. Possible
7. Hoped.
8. Not certain
9. Doubtful
10. Impossible

Question 4

What is the definition of probability?

Answer 4

The chance that an uncertain event will occur (0-1)

Question 5

What is an impossible event?

Answer 5

An event that has no possibility of occurring (0)

Question 6

What is a certain event?

Answer 6

An event that is sure to occur (1)

Question 7

What is priori probability?

Answer 7

Based on prior knowledge, we know all the possible outcomes and they are all equally likely e.g tossing a coin

Question 8

How is probability occurrence calculated for a priori?

Answer 8

no. of ways event occurs/total possible outcomes

Question 9

What is empirical probability?

Answer 9

Based on observed data, e.g experiments, surveys

Question 10

How is probability occurrence calculated for empirical data?

Answer 10

no. of ways event occurs/total possible outcomes

Question 11

What is subjective probability?

Answer 11

Based on combinations of past experiences, personal opinion, and analysis of a particular situation

Question 12

How is it possible to distinguish between empirical probability and priori probability when you can conduct experiments for a priori?

Answer 12

If you tossed a coin several times, it would be unlikely to produce 1/2. However, if done an infinite number of times it would produce a 1/2. Probability only becomes priori after many experiments.
- For empirical experiments, you would look at number of trials rather than no. outcomes

Question 13

When is subjective probability useful considering that if you ask two people you will get two different outcomes?

Answer 13

• No previous data

- When empirical/priori cannot be computed

Question 14

What is the sample space?

Answer 14

Collection of all possible outcomes

Question 15

What is an experiment?

Answer 15

Any procedure where the outcome is unknown

Question 16

What are events?

Answer 16

Each possible outcome of a variable is an event

Question 17

What is a simple event?

Answer 17

An event described by 1 characteristic e.g a day in January

Question 18

What is a joint event?

Answer 18

An event described by two or more characteristics e.g a day in Jan that is also a Wednesday

Question 19

What is a complement of A?

Answer 19

All events that are not part of event A, e.g all days in 2015 that are not January

Question 20

What is marginal probability?

Answer 20

Refers to the probability of a simple event e.g January when given a contingency table showing 2 variables. e.g Table shows days in Jan, not Jan, Wed, not Wed but we are only interested in Jan.

Question 21

What does marginal probability always correspond to in terms of a contingency table?

Answer 21

Always corresponds to row or column totals in a contingency table

Question 22

What does joint probability correspond to in a contingency table?

Answer 22

Refers to values within the contingency table rather than the row or column totals.

Question 23

How is the probability of joint event A and B computed?

Answer 23

P (A and B) = the number of outcomes satisfying A and B/total outcomes

Question 24

How is the marginal probability of event A calculated when given A and B in a contingency table?

Answer 24

P (A) = P (A and B) + P (A1 and B2) +….+ P (A and Bk)
P (wed) = P ( wed and jan) + P (wed and feb) +…+ P (wed and dec)
NOTE - all these months are mutually exclusive and collectively exhaustive

Question 25

What are mutually exclusive events?

Answer 25

Events that cannot occur simultaneously e.g Jan and not Jan. The joint probability of mutually exclusive events is 0 as they cannot occur together.

Question 26

What are collectively exhaustive events?

Answer 26

If the two events cover the entire sample space. One of the events must occur. The sum of collectively exhaustive events is 1. e.g Jan and not Jan

Question 27

What is the general addition rule?

Answer 27

P (A or B) = P (A) + P (B) - P (A and B)

P (Jan or Feb) = P (Jan) + P (Feb) - P (Jan and Feb)

Question 28

What does the general addition rule mean?

Answer 28

The union of the two events is equal to the summation of their marginal probabilities minus their joint probability. Union is denoted by OR and joint is denoted by AND.