The document discusses experimental and theoretical probability. It provides an example of calculating the theoretical probability of having 2 girls in a family with 3 children. The theoretical probability is calculated as 1/4 or 25% since there are 4 possible combinations (BBB, BBG, GBB, BGG) and only 1 of those combinations results in 2 girls.

1. Experimental and Theoretical Probability
In a family of three children, what is the probability that 2 of the children will be girls?
one two three

2. In a family of three children, what is the probability that 2 of the children will
be girls?
Experimental Probability: The chances
of something happening, based on
repeated testing and observing results. It is
the ratio of the number of times an event
occurred to the number of times tested.
For example, to find the experimental
probability of winning a game, one must
play the game many times, then divide the
number of games won by the total number
of games played.

3. In a family of three children, what is the probability that 2 of the children will
be girls?
Theoretical Probability: The chances of
events happening as determined by
calculating results that would occur under
ideal circumstances. For example, the
theoretical probability of rolling a 4 on a
four-sided die is 1/4 or 25%, because there
is one chance in four to roll a 4, and under
ideal circumstances one out of every four
rolls would be a 4. Contrast this with
experimental probability.

4. In a family of three children, what is the probability that 2 of the children will
be girls?
Theoretical Probability

5. Binomial Experiments & Probability
DICTIONARY
Simulating Binomial Experimets: randBin(# of trials, prob. of success, # of simulations)
What is the probability of getting exactly 2 heads when fliping 3 coins 40 times?
You'll need to know the the theoretical probability of this result is 3/8.
Here is how to do the experiment on your calculator.
Step Action
1. Press [Math] button on TI83 calculator.
2. Select [Prob].
3. Select [randBin] (random binomial experiment).
4. Type in (1, 3/8, 40) .
1 represents the outcome for success (failure is 0). little predator
3/8 represents the theoretical probability of success.
40 represents number of times the experiment is repeated.
5. Press enter and a result will show in row.
6. Press [STO] [2nd] [L1] to store the results in List 1.
7. Press [2nd] [STAT].
8. Select [MATH] [Sum] [2nd] [L1] to find the sum of all the values in List 1.
9. Since quot;success = 1quot; and quot;failure = 0quot; this sum represents the number of successes.
You can also use this website: Random.org http://www.random.org/

6. HOMEWORK
What is the probability of spinning each of the following using the
spinner shown? The colours on the spinner are red, yellow, and blue.
1. P(red)
2. P(yellow)
3. P(green)
4. P(red, yellow or blue)
5. P(not red)

7. HOMEWORK
Design an experiment using coins to simulate a 10 question true/false test.
What is the experimental probability of scoring at least 70% on the test if
you guess each answer?

8. HOMEWORK
Design an experiment to determine the probability of passing a six-question
multiple choice test if you guess all the answers. Each question has four
answers, and one answer is correct in each case.
How many simulations would seem reasonable?
What is the experimental probability of getting at least 50% on the test?