Probability Starters NCEA Results Year 12 and 13

Probability Starters

NCEA Results Year 12 and 13 students were surveyed about their NCEA results. Passed L 1 Year 12 Year 13 Still to achieve M 25 30 F 22 23 M 25 15 F 55 5 A student is chosen at random. Calculate the following probabilities. 1. The student has passed level 1. 2. A girl has not achieved level 1. 3. The student is a female at year 12. 4. A student who has passed is a girl in year 12. 5. The student is a year 13 boy who is still to achieve. 6. A boy is chosen, what is the probability that he has passed?

Dominos A full set of dominos contains all the possible pairs of numbers from 1 to 6 plus blanks. 1. How many dominos are there in a full set? 2. If one domino is selected at random from a full set, what is the probability it has exactly six dots on it?

I have a bag and in it are 4 beans, 2 are yellow and 2 are blue. If I draw two beans from the bag what is the probability that they are both blue?

I have a bag and in it are 7 beans, 2 are yellow and 5 are blue. If I randomly select two beans from the bag what is the probability of getting one of each colour. If one of the beans is yellow what is the probability that the other bean is blue?

Simulation • A simulation imitates a real situation. • It should act as a predictor of what would actually happen in practice. • It is a model in which experiments are carried out so as to estimate what might happen in real life.

Simulation using the Calculator • The random number generator on the calculator produces 3 digit random numbers between 0. 000 and 0. 999 all equally likely. • For each digit there are 10 possible outcomes. What are they? • These digits can be used on their own or together to simulate outcomes for probability experiments.

Example • Using the first two digits only of a random number we can model or simulate a two child family. • An odd digit represents a girl. (p= ) • An even digit represents a boy. • So the random number 0. 234 will represent the family of boy(2) then girl(3), ignore the 4.

Simulation • When a child is born it is equally likely to be a boy or a girl. • Use the random number function on your calculator to simulate a three child family. • Repeat 9 more times. (10 families in total) • Use your data to estimate the proportion of three child families which have all children the same sex.

Three Child Families Simulation TOOL Using the random number function of the calculator. Using the 3 digits of a random number. An odd digit will represent a boy and an even digit will represent a girl. Even and odd occur with equal probabilities same as boys or girls) TRIAL Generate a random number to represent the three members of the family. Record the results. Eg. 0. 479 will be recorded as GBB (even, odd) Repeat the trial 10 times. RESULTS BGB GBB GGB BBG GBB GBG BBB CALCULATION Probability of a family being all the same sex is 0. 2 (2 from 10)

TRAFFIC LIGHT SIMULATION Coming to school each day, Laura rides through 2 traffic lights. The probability that any one light is green is 0. 3, and the probability that it is not green is 0. 7 Design and carry out a simulation to estimate the probability that Laura will find that both lights are green.

TTRC • Tool – Using calc random number function. – Using the first 2 digits to represent each traffic light. – If the digit is 1 or 2 or 3 the light is green, otherwise it is red. • Trial – Generate one random number to represent one trip to school. – Record the result. – Example 0. 386 will be green (3) red (8) ignore the 6. • Results – Set results out in a table trip lights • Calculations – From my results we can see that Laura got two greens XX% of the time.