Mathematics
Grade 7
15 min
Probability of independent and dependent events
Probability of independent and dependent events
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1
Introduction & Learning Objectives
Learning Objectives
Define and differentiate between independent and dependent events.
Identify real-world scenarios as involving independent or dependent events.
Calculate the probability of two independent events occurring.
Calculate the probability of two dependent events occurring.
Explain how 'replacement' affects whether events are independent or dependent.
Solve word problems involving the probability of combined independent and dependent events.
Have you ever wondered what the chances are of winning two prizes in a row, or picking your favorite candy twice from a bag? 🤔 Let's explore how we can figure out these probabilities!
In this lesson, you'll learn about two special types of events: independent and dependent. Understanding the difference i...
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Key Concepts & Vocabulary
TermDefinitionExample
ProbabilityThe measure of how likely an event is to occur. It's a number between 0 (impossible) and 1 (certain).The probability of flipping a coin and getting heads is 1/2.
EventA specific outcome or a set of outcomes in an experiment.Rolling a 4 on a six-sided die is an event. Rolling an even number is also an event.
OutcomeA single possible result of an experiment.When you flip a coin, 'heads' is one outcome, and 'tails' is another outcome.
Independent EventsTwo events are independent if the outcome of the first event does NOT affect the outcome of the second event.Flipping a coin and getting heads, then rolling a die and getting a 6. The coin flip doesn't change the die roll.
Dependent EventsTwo events are dependent if the outcome of...
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Core Formulas
Basic Probability Rule
$$P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$
This rule is used to find the probability of a single event occurring. You count how many ways your desired outcome can happen and divide by the total number of possible outcomes.
Probability of Independent Events (AND Rule)
$$P(A \text{ and } B) = P(A) \times P(B)$$
To find the probability that two independent events, A and B, both happen, you multiply the probability of event A by the probability of event B. The first event does not change the possibilities for the second event.
Probability of Dependent Events (AND Rule)
$$P(A \text{ and } B) = P(A) \times P(B \text{ after } A)$$
To find the probability that two dependent events, A and B...
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Challenging
A bag contains 'r' red marbles and 'b' blue marbles. If you draw two marbles without replacement, which expression represents the probability of drawing two blue marbles?
A.(b * (b-1)) / ((r+b) * (r+b-1))
B.(b * b) / ((r+b) * (r+b))
C.(b * (b-1)) / (r * (r-1))
D.b / (r+b)
Challenging
A cooler contains 12 sodas: 5 colas, 4 root beers, and 3 orange sodas. You grab three sodas one after another without looking. What is the probability of grabbing three colas in a row?
A.60/1320
B.125/1728
C.60/1728
D.15/1320
Challenging
A bag has 3 red and 4 blue marbles. Consider two probabilities: P(A) is the probability of drawing red then blue without replacement. P(B) is the probability of drawing blue then red without replacement. Which statement is true?
A.P(A) = P(B)
B.P(A) > P(B)
C.P(A) < P(B)
D.There is not enough information to compare P(A) and P(B).
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