This comprehensive review worksheet covers key probability concepts crucial for success on your Common Core Math 2 probability test. We'll delve into both theoretical and experimental probability, conditional probability, and independent and dependent events. Let's get started!
I. Theoretical Probability
Theoretical probability is the likelihood of an event occurring based on logical reasoning and the possible outcomes. It's calculated as:
P(event) = (Number of favorable outcomes) / (Total number of possible outcomes)
Example: What is the theoretical probability of rolling a 3 on a standard six-sided die?
There is one favorable outcome (rolling a 3) and six possible outcomes (1, 2, 3, 4, 5, 6). Therefore, P(rolling a 3) = 1/6.
Practice Problems:
- What is the theoretical probability of drawing a red card from a standard deck of 52 playing cards?
- A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the theoretical probability of drawing a blue marble?
- What is the theoretical probability of flipping a coin twice and getting two heads?
II. Experimental Probability
Experimental probability is determined through conducting an experiment and observing the results. It's calculated as:
P(event) = (Number of times the event occurred) / (Total number of trials)
Example: A coin was flipped 100 times, and heads appeared 53 times. What is the experimental probability of getting heads?
The event (getting heads) occurred 53 times out of 100 trials. Therefore, P(heads) = 53/100 = 0.53.
Practice Problems:
- A basketball player made 15 out of 20 free throws. What is the experimental probability of the player making a free throw?
- A spinner was spun 50 times, landing on red 12 times, blue 18 times, and green 20 times. What is the experimental probability of the spinner landing on blue?
III. Conditional Probability
Conditional probability refers to the probability of an event occurring given that another event has already occurred. It's denoted as P(A|B), which reads "the probability of A given B." The formula is:
P(A|B) = P(A and B) / P(B)
Example: A bag contains 4 red marbles and 6 blue marbles. What is the probability of drawing a red marble given that the first marble drawn was blue (and not replaced)?
Initially, there are 10 marbles. The probability of drawing a blue marble first is 6/10. After drawing one blue marble, there are 9 marbles left, with 4 red marbles. The probability of drawing a red marble second is 4/9. Therefore, P(Red|Blue) = (4/10) / (6/10) = 4/6 = 2/3
Practice Problems:
- A box contains 3 red pens and 5 blue pens. What is the probability of drawing a red pen, given that the first pen drawn was blue (and not replaced)?
- In a class of 25 students, 15 are girls and 10 are boys. If two students are selected at random without replacement, what is the probability that the second student selected is a girl given that the first student selected was a boy?
IV. Independent and Dependent Events
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Independent Events: The outcome of one event does not affect the outcome of another event. P(A and B) = P(A) * P(B)
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Dependent Events: The outcome of one event affects the outcome of another event. The probability of the second event depends on the outcome of the first event. (Example: drawing marbles without replacement).
Practice Problems:
- Are the events of rolling a die and flipping a coin independent or dependent?
- Are the events of drawing two cards from a deck without replacement independent or dependent? Explain.
This review worksheet provides a solid foundation for your Common Core Math 2 probability test. Remember to practice these concepts and seek clarification on any areas where you feel less confident. Good luck!
