Probability Math Help

Learning Objective:

• Recognize that in a probability experiment there are n equally likely events. • Recognize that the n equally likely events make up the complete list of possible outcomes for an experiment. • Select one event and identify the favorable outcomes of it occurring. • Use the theoretical definition to find the probability of an event occurring.

Helpful Hints:

Probability is the likelihood of a particular outcome occurring.

Definitions:

1. Probability = number of favorable outcomes total number of possible outcomes

2. Probability Experiment – an investigation or number of trials in search of all possible outcomes (results) of an event occurring.

e.g. What are all the possible outcomes when rolling a pair of dice?

3. Event - any set of outcomes (results) from an experiment.

e.g. Heads and tails are the set of outcomes resulting from the event of tossing a coin.

4. Outcome – a possible result of an experiment or trial.

e.g. When tossing 1 coin, a possible outcome or result is tails.

5. Possible Outcomes – a list of all the resulting possibilities from an event.

e.g. When rolling a die – all possible outcomes are 1, 2, 3, 4, 5, 6.

6. Favorable Outcome – the result that is desired.

e.g. Roll a 4 on a die → 4 is the only favorable outcome.

Statistics and Probability / Probability / Object Interactive / Math Help

Examples from the “Explore It” mode:

Selected: A tree diagram of 2 coins tossed.

First Coin (brown area): may result in the outcome of a head or tail. Second Coin (blue): a head or tail could follow each toss of the first coin.

Show Me: Individual Outcome Highlighted Favorable Outcome, Head followed by Head → H, H Total Number of Favorable Outcomes = 1

Possible Outcomes:

-the first outcome of heads could be followed by a head or a tail -the first outcome of tails could be followed by a head or a tail.

All possible outcomes are listed below: Head followed by a head: H, H Head followed by a tail: H, T Tail followed by a head: T, H Tail followed by a tail: T, T

Total Number of Possible Outcomes = 4

Probability = number of favorable outcomes___ total number of possible outcomes

Statistics and Probability / Probability / Object Interactive / Math Help

1 Event Probability (of head followed by a head) = 4

Selected: A tree diagram showing 2 spinners. First Spinner (brown area): may result in the outcome white, red, or blue Second Spinner (blue area): a white, red, or blue can follow each of the outcomes of the first spinner.

Show Me: Individual Outcome Highlighted Favorable Outcome, white followed by white → W, W Total Number of Favorable Outcomes = 1

Possible Outcomes: the results of all color combinations of the 2 spinners. Total Number of Possible Outcomes = 9 1 Event Probability (of having 2 whites) = 9

Statistics and Probability / Probability / Object Interactive / Math Help

Selected: A chart diagram of dice rolled.

First Die (brown area): may result in the outcomes 1, 2, 3, 4, 5, or 6. Second Die (blue area): 1, 2, 3, 4, 5, and 6 can follow each outcome of the first die.

Show Me: Individual Outcome Highlighted Outcome, 1 followed by 1 → 1, 1 Total Number of Favorable Outcomes = 1

Possible Outcomes: the results of all tosses of the first die combined with the second. Total Number of Possible Outcomes = 36

1 Event Probability (of 1 followed by 1) = 36

Statistics and Probability / Probability / Object Interactive / Math Help

Selected: A chart diagram of a coin and a spinner.

Coin (brown area): the toss results in the outcome heads or tails. Spinner (blue area): color outcomes white, red, or blue can follow each toss of the coin.

Show Me: Blue Highlighted outcomes, a coin toss followed by the blue color. Head, Blue → H, B Tail, Blue → T, B Total Number of Favorable Outcomes = 2

Possible Outcomes: the results of a head or tail followed by each color on the spinner. Total Number of Possible Outcomes = 6 2 1 Event Probability (of a coin toss with the color blue) = = 6 3

Statistics and Probability / Probability / Object Interactive / Math Help

Selected: A chart diagram of a spinner and a die.

Spinner (brown area): the spin results in the outcomes white, red, or blue. Die (blue area): the outcomes 1, 2, 3, 4, 5, or 6 can follow each color of the spin.

Show Me: A number less than 3. Highlighted outcomes show each colour with either a 1 or 2. W, 1 R, 1 B, 1 W, 2 R, 2 B, 2 Total Number of Favorable Outcomes = 6

Possible Outcomes: -the results of a head or tail followed by each number from 1 to 6. Total Number of Possible Outcomes = 18 6 1 Event Probability (of a colour followed by a number less than 3) = = 18 3

Statistics and Probability / Probability / Object Interactive / Math Help