Probability Concepts

Question 1

What is Probability Concepts?

Answer 1

The probability of an event, X occurring is expressed as a decimal or a fraction from 0-1

Question 2

How do we express the probability of an event occurring?

Answer 2

P(# of thing) = # of favourable outcomes / total # of outcomes

Question 3

What does P(A n B) mean?

Answer 3

And

Question 4

What does P(A/B) mean?

Answer 4

Out of

Question 5

What does P(A u B) mean?

Answer 5

Or

Question 6

What does P(A’) mean?

Answer 6

Not A

Question 7

What does P(A u B/C) mean?

Answer 7

Or Out of

(A or B out of C)

Question 8

How do we write: What is the probability of A or B?

Answer 8

P(A u B)

Question 9

How do we write: What is the probability of A and B?

Answer 9

P(A n B)

Question 10

How do we write: What is the probability of Everything but A?

Answer 10

P(A’)

Question 11

How do we write: If B happens what is the probability of A?

Answer 11

P(A/B)

Question 12

How would you write the probability for this question: If a student studies English what is the probability they study Psychology?

Answer 12

P(pyschology/english)

Question 13

How do we write: What is the probability that A and B are ‘mutually exclusive’?

Answer 13

P(A n B) = 0

Question 14

What does ‘mutually exclusive mean’?

Answer 14

If events A and B are mutually exclusive, either one happens or the other happens (they don’t both happen).

Question 15

How do we write: What is the probability that 2 events are independent?

Answer 15

P(A n B) = P(A) x P(B)

Question 16

What does it mean if events are independent?

Answer 16

If 2 events are independent i.e the outcome of one has no influence on the outcome of the other.

Question 17

What is the ‘multiplication principle’?

Answer 17

When you want to know the probability of something happening you multiply the probabilities to find the total number of outcomes.
E.g if you roll 2 dice and want to know the probability of rolling 2 fives, you would multiply the probabilities of getting a five on each dice.

P(5,5) = 1/6 x 1/6 = 1/36
(note the 2 rolls are independent)

Question 18

Using the ‘multiplication principle’ how would you answer this question: In year 10 students have 3 option lines.
1) Japanese, French, Te Reo.
2) Textiles, Food Tech
3) Graphics, D.I.T, Art, Hard Tech
How many different combinations are there?

Answer 18

3 x 2 x 4 = 24

Question 19

Using the ‘multiplication principle’ how would you answer this question: If you roll 3 dice how many possible outcomes are there?

Answer 19

6 x 6 x 6 = 216

Question 20

Using the ‘multiplication principle’ how would you answer this question: 5 people on a bench side by side. How many ways are there of arranging 5 people on a bench?

Answer 20

5 x 4 x 3 x 2 x 1 = 120
or 5! = 120
(! = factorial)

Question 21

What is ‘experimental probability’?

Answer 21

When you use an experiment or past data to find a probability.
E.g In the last 56 games the All Blacks have won 43, therefore what is the probability they win their next game?
P(win) = 43/56 = 0.768 (3dp)

Question 22

What is ‘theoretical probability’?

Answer 22

Probability that we can predict.
E.g Rolling a 3 when rolling a dice.
P(3) = 1/6
* the 1 is the 1 x 3 on dice
* the 6 is the total numbers on the dice
* P(X=3) means the same as P(3)
* P(X<4)=3/6=1/2(=0.5)
* P(X≥3)=4/6=2/3(=0.667(3dp))

Question 23

If a card was drawn randomly from a deck what is the probability that it is a king?

Answer 23

P(X=king) = 4/52 = 1/13 = 0.077 (3dp)

Question 24

If a card was drawn randomly from a deck what is the probability that it is a red card?

Answer 24

P(X=red card) = 1/2

Question 25

If a card was drawn randomly from a deck what is the probability that it is a number less than or equal to 4?

Answer 25

P(X=≤ 4) = 16/52 = 4/13

Question 26

If a card was drawn randomly from a deck what is the probability that it is a 6 and a club?

Answer 26

P(6 and club) = 1/52

Question 27

If a card was drawn randomly from a deck what is the probability that it is a 3 or a heart?

Answer 27

P(3 or heart) = 16/52 = 4/13

Question 28

What are the 3 things you need to do when working with probabilities?

Answer 28

• Know your TOTAL
• If using probabilities your total is 1. These might be displayed in a table or graph (probability distribution)
  *If using frequencies (whole numbers) then make sure you know how many in total.

Question 29

What are the 4 steps you do to answer this question: Let X=number of children in a household?

Answer 29

1) Draw the probability distribution table (remembering TOTAL MUST EQUAL 1).

2) Find the value of k

3) Draw a graph of the probability distribution

4) Then do all the calculations to get your answer

Question 30

A group of Year 13’s were surveyed about their plans for the following year. Find the probability that: a. P(uni) b. P(uni u tech)

Plan Frequency
Uni 52
Tech 13
Trade 8
Job 9
Travel 11
Other 3
Total 96

What were the probabilities for each of the plans?

Answer 30

a. P(uni) = 52/96 = 13/24 (=-.54(2dp))

b. P(uni u tech) = 65/96 (=0.68(2dp))

Probabilities:
Uni: 52/96 = 0.54
Tech: 13/96 = 0.14
Trade: 8/96 = 0.08
Job: 9/96 = 0.09
Travel: 11/96 = 0.11
Other: 3/96 = 0.03

Question 31

What is a two way table?

Answer 31

A Two way table also known as a table of counts has 2 variables in a group. The numerator is the top and the denominator is the total.

Question 32

What is a Venn diagram?

Answer 32

3 interlocking circles used to help order our groups.

Question 33

What is ‘relative risk’?

Answer 33

Relative Risk is used when comparing two probabilities, it is often referred to as finding true relative risk.

E.g If the probability of getting food poisoning from a food truck is 0.075 i.e P(food poisoning/food truck)=0.075 and the probability of food poisoning from a restaurant is 0.024 i.e P(food poisoning/restaurant)=0.024 then comparing these two; the relative risk or RR=P(A) / P(B)
so RR=0.075 / 0.024 = 3.1 (1dp) Therefore a person is 3.1 times AS likely to get food poisoning from a food truck than from a restaurant.

Question 34

What are tree diagrams or probability trees?

Answer 34

Another tool to help calculate probabilities. It is useful when there is a sequence of events or when a group is split into subgroups then those subgroups are split again.

Question 35

What are the 6 tips on tree diagrams?

Answer 35

1) Read left to right
2) Probabilities (decimals or fractions) on the branches
3) Outcomes at end of branches
4) Each set of branches contain probabilities that add to 1
5) Multiply across the branches to find the probability of a sequence of outcomes
6) Add favourable outcomes to answer a question

Question 36

What is the equation for Expected Number?

Answer 36

probability x total

Question 37

What is the equation for Independence?

Answer 37

P(A n B) = P(A) x P(B)

Question 38

What is the equation for Mutually Exclusive?

Answer 38

P(A n B) = 0

Question 39

What will a truly random sample be?

Answer 39

Unbiased

Question 40

The bigger the sample the more _____________ you can have of your findings?

Answer 40

CONFIDENCE

Question 41

what number is considered statistically sufficient as a sample size to make an inference?

Answer 41

30

Question 42

What does a ‘random sample’ mean?

Answer 42

Each member of the population has the same chance of selection

Question 43

Randomness in _____________ means events are _____________ of each other (i.e a previous outcome does not affect the probability that an event will occur).

Answer 43

• PROBABILITY
• INDEPENDENT

Question 44

What is a Simulation?

Answer 44

A simulation imitates true probability using coins, cards, dice random number generator, spinners etc. It must be repeated a LOT of times.