18 Questions
What is the main difference between theoretical and experimental probability?
Theoretical probability is what we expect to happen, while experimental probability is what actually happens when we try it out.
For the coin toss experiment with Lisa, Tom, and Al, what is the theoretical probability of getting heads?
$\frac{20}{50}$
In the dice game where landing on '1' results in getting a letter for the word 'SKUNK', what does theoretical probability help determine?
The likelihood of losing the game
What principle should be applied when calculating the theoretical probability for a game like the 'SKUNK' dice game?
Law of Large Numbers
How can theoretical and experimental probabilities be related in real-world scenarios?
Theoretical probability helps in predicting outcomes, while experimental probability verifies these predictions.
'Random Task' mentioned in the text refers to:
A task that involves some degree of randomness or uncertainty
What is the correct probability of Greg throwing a knuckleball for a strike?
0.2
What is the probability that the dessert does not have peanut butter in it?
0.8
What is the chance that the dessert is brownies and has peanut butter in it?
0.06
In an independent activity, if you flip a coin three times, what's the probability you will get tails on at least one of the flips?
1
What is the sum of all possible outcomes' probabilities in a single round of rock, paper, scissors between two players?
1
What is the probability of Greg throwing a fastball for a strike?
0.06
What is the probability that Greg will throw a knuckleball for a strike?
0.2
If Greg throws 100 pitches, how many of them, on average, will be knuckleballs?
20
What is the probability that Greg will throw a fastball for a strike?
0.6
If Greg throws 90 fastballs, how many of them, on average, will be strikes?
54
What is the probability that Greg will throw a knuckleball and it won't be a strike?
0.4
If Greg throws 80 knuckleballs, how many of them, on average, will not be strikes?
48
Study Notes
Theoretical and Experimental Probability
- Theoretical probability is what we expect to happen, whereas experimental probability is what actually happens when we try it out.
- The probability is still calculated the same way, using the number of possible ways an outcome can occur divided by the total number of outcomes.
Law of Large Numbers
- No information is provided about the Law of Large Numbers in the given text.
Probability of Greg Throwing a Strike
- The probability of throwing a fastball for a strike is 0.6.
- The probability of throwing a knuckleball for a strike is 0.2.
- On average, for every 10 pitches, 7 of them are fastballs (0.7 probability) and 3 of them are knuckleballs (0.3 probability).
- The probability of Greg throwing a strike is 0.48 or 48%.
Coin Tossing Experiment
- Three students tossed a coin 50 times individually, with varying results (Lisa: 20 heads, Tom: 26 heads, Al: 28 heads).
- The theoretical probability of getting a head is not explicitly stated, but it is typically 0.5.
Dice Game
- The game involves rolling a dice, and if a player lands on '1', they get a letter.
- If a player spells the entire word 'SKUNK', they lose the game.
- The theoretical probability of losing the game can be calculated using probability theory.
Tree Diagrams
- Tree diagrams can be used to show the probability of different outcomes.
- Example: The probability of Greg throwing a fastball or a knuckleball, and the probability of each pitch being a strike.
- The sum of the probability outcomes in a tree diagram must equal 1.
Independent and Dependent Questions
- Independent questions: Imagine flipping a coin three times. What's the probability you will get a head on at least one of the flips?
- Dependent questions: Combine the probability of different outcomes to find the overall probability of an event.
Test your knowledge on theoretical and experimental probability in this quiz covering the concepts of what we expect to happen versus what actually happens when an experiment is conducted, as well as how to calculate probabilities based on possible outcomes. This quiz is based on Lesson Three of a data management course.
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