Theoretical Probability
Show the formula for calculating the theoretical probability of an event occurring.
P= number of favourable outcomes / total number of outcomes
State the independent variable
The prices of houses being sold in a suburb during the first quarter of a year and the number of bedrooms in those houses.
Independant = number of bedrooms
Explain the difference between simple and compound interest.
Simple interest you only earn/pay interest on the principal amount.
When compounding interest is paid on the principal plus and interest earned in previous compounding periods.
H | T
H| HH | HT
T| TH | TT
What is the ratio used to determine the gradient of a straight line?
Identify the sample space for flipping a coin
{Heads, Tails}
State the dependant and independent variable.
The price of an Action Man toy in a number of different toyshops and the number of these toys bought from each shop within a particular week
The price of an Action Man toy in different shops is the independent variable and the number of these toys bought from each shop is the dependent variable.
Calculate the total amount repaid on a simple interest loan over 5 years at 6.25% interest when $15,000 is borrowed.
I = $4687.50
A = $19687.5
Draw a blank array to list the outcomes of rolling an 8-sided die and spinning a 3 coloured spinner with Red, Blue and Black.
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Red |
Black |
Blue |
List the sample space of the following;
An arrow is shot at a target where there is a blue area, a white area, a red area and a black area.
{blue, white, red, black}.
A pack of 52 playing cards is shuffled, and one card is drawn. What is the probability that the card will be a red queen?
*BONUS points for simplifying
P(red queen) = 2/52
*Simplified = 1/26
Name the dependant variable & what is expected to happen to the dependant variable if the independent variable increases?
Value of a car and its age
The value is dependant
As the age of a car increases, its value is expected to decrease.
What is the value of a $60,000 investment at the end of 10 years, earning 5.5% interest compounding.
$102488.66
Identify the formula to calculate the relative frequency of a trail.
Relative Frequency = number of succesful trials / total number of trials
It is estimated that 88% of the population vaccinate their kids.
In a population of 300 individuals, approximately how many individuals can we assume have vaccinated their children?
264
A standard six-sided die is rolled. What is the probability of rolling a 3.
P (3) = 1/6
y = 5x - 4
If x = 2; solve for y
6
Calculate the interest rate when $750,000 is paid in interest over a 30-year loan period when the principal mortgage value was $600,000. (simple interest)
4.1%
Candidate | 1 | 2 | 3 | 4 |
Number of voters who preferred this candidate
| 115 | 168 | 145 | 72 |
Estimate the probability of candidate number 4 winning the election - answer as a decimal.
0.144
Sandra is buying a $9000 TV and needs to borrow 90% of the value to complete the purchase. The loan attracts 15% simple interest and is over 4 years. How much will Sandra pay back for the loan?
*Bonus points for calculating the total amount paid for the tv.
Deposit = $900
Loan amount = $8100
I = P x i x n
I = 8100 x 0.15 x 4
I = 4680
A = P + I
A = $8100 + $4680
A = $12780
Total paid for the TV = $900 + $12780 = $13680
Eli’s Maths teacher told him that he had a 70% chance of passing the final exam, based on Eli’s prior exam scores.
Identify the complement of this event and the probability of the complementary event occurring.
The complement to Eli passing the exam is not passing the exam.
P = 30%
y = 4x - 11
What is the Y-intercept and Gradient values?
Gradient = 4 or 4/1
Y-intercept = -11
Compare which of the following options will result in a larger investment at maturity when $50000 is invested for 8 years.
2.5% compounding
3% simple
Which is the better option?
Compounding = $60,920.144
Simple = $62,000
The simple interest is better value.
At a restaurant you can choose a two-course meal out of the following options;
Main: Chicken, Fish or Vegetarian
Dessert: Ice Cream, Cheesecake, Fruit
Draw a tree diagram to show all possible outcomes.
Main
- Ice Cream
Chicken - Cheesecake
- Fruit
- Ice Cream
Fish - Cheesecake
- Fruit
- Ice Cream
Vegetarian - Cheesecake
- Fruit
If y represents any number write the expression for 3 times that number.
3 x y = 3y