Theoretical
Keith is playing a board game in which he spins a spinner to determine how many spaces to move his game piece. He is 3 spaces away from the finish and can only move forward if he spins a 1, 2, or 3 on his next turn. All sections of the spinner have the same size. What is the probability that Keith moves forward on his next turn if the spinner includes: 5, 1, 3, 4, 1, and 2?
4/6 = 67%
A kicker made 10 out of his last 12 field goal attempts. Predict about how many of his next 42 field goal attempts the kicker will not make.
2/12 missed field goals = 17%. 0.17 * 42 = 7 field goals.
Define "outcome."
What can happen in an experiment.
Shawn places 1 red, 1 blue, 1 black and 1 green sock in a bag. He selects a sock without looking, records the color, and puts the sock back in the bag. His results are: he chooses 8 red, 4 blue, 5 green, and 7 black. How does the experimental probability of choosing a green sock compare to the theoretical probability?
Theoretical Probability = 1/4 = 25%
Experimental = 5/24 = 21%
A teacher brings in bagels for her students. There are 4 everything bagels, 6 sesame seed bagels, and 8 whole wheat bagels in the bag. What is the probability that a bagel that is randomly selected is whole wheat?
8/18 = 44%
Rita selects a marble without looking, records the color, and returns the marble to the bag. In 25 trials, she selects a green marble 10 times. She selects a blue marble the other times. What is the most reasonable prediction for how many times Rita will select a blue marble in 100 trials?
15/25 = 0.6 * 100 = 60 times.
Define "event."
A set of one or more outcomes
How could the experimental probability of an event more closely match the theoretical probability?
Conducting many trials - the more trials conducted, the more likely the two probabilities will be similar.
Magdalena records the eye color of everyone on her soccer team (4 - blue, 1 - green, 15 - brown). What is the probability of randomly selecting a person with blue eyes? Green eyes? Brown eyes?
Blue - 4/20 = 20%
Green - 1/20 = 5%
Brown - 15/20 = 75%
A letter tile is randomly selected from a bag, recorded, and replaced 100 times. The results are listed below. What is the experimental probability of selecting the letter "E"? A = 16 E = 11 I = 29 O = 19 U = 25
11/100 or 0.11, or 11%
The theoretical and experimental probabilities for the same outcome of an experiment (e.g. flipping a coin) will sometimes differ. Why could this happen?
Experimental probability is based on the results of an experiment. The number of trials will affect the probability.
Each player on a softball team will get a uniform with a randomly selected number between 1 and 30. No two players will have the same number. The first player to get a uniform thinks the probability the she will get a single-digit number is 9/10. Is the player correct? If not, what is the correct probability?
No - the correct probability is 9/30, or 30%.
Define "experimental probability."
The probability of what actually occurs.
The theoretical probability of tossing a coin and having it land heads up is 1/2. Tori tosses a coin 50 times and her brother tosses a coin 120 times. Whose experimental probability of having a coin land heads up will likely be closer to 1/2?
The brother - the more trials you have, the closer the experimental probability will be to the theoretical probability.
A bag contains several marbles. The theoretical probability of selecting a green marble at random is 1/8. Orion draws a marble from the bag without looking, records the color, and replaces it. He does this 10 times and never draws a green marble. Does this mean there are no green marbles in the bag?
No - the theoretical probability proves there is one green marble out of the 8 possible choices.
Matt has a multi-colored pack of pens. At the start of each class, he randomly selects a blue, black, purple, or red pen from the pack and replaces it after class. Over the last 16 classes, he chose 7 blue pens, 5 black pens, 3 purple pens, and 1 red pen. Is it likely that there are equal numbers of each color pen in the pack?
No - of this was the case, each pen would be selected about 25% of the time. The frequencies range from 1 to 7, so it isn't likely.
Define "theoretical probability."
It is the probability of what should occur.
Describe an event involving a standard number cube (1-6) for which the experimental probability and theoretical probability are both equal to 1/3.
Possible Answer: You roll a number cube 30 times and you roll a 5 or 6 on 10 out of 30 rolls. The experimental probability of rolling a 5 or 6 is 10/30, or 1/3. The theoretical probability is 2/6, or 1/3.