Mathematics
Grade 7
15 min
Probability of dependent and independent events
Probability of dependent and independent 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 either independent or dependent events.
Calculate the probability of two independent events occurring.
Calculate the probability of two dependent events occurring.
Explain how 'with replacement' and 'without replacement' affect event dependency.
Apply probability rules to solve multi-step problems involving combined events.
Have you ever wondered about the chances of winning two games in a row, or picking your favorite candy twice from a bag? 🤔 Let's explore how we figure out these probabilities!
In this lesson, you'll learn about different types of events and how their outcomes can affect each other. Understanding...
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Key Concepts & Vocabulary
TermDefinitionExample
ProbabilityThe measure of how likely an event is to occur. It's expressed as a fraction, decimal, or percentage between 0 and 1 (or 0% and 100%).The probability of flipping a coin and getting heads is $\frac{1}{2}$.
EventA specific outcome or a set of outcomes in an experiment or situation.Rolling a '4' on a number cube is an event. Rolling an 'even number' is also an event.
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 flipping it again and getting heads. The first flip doesn't change the chances of the second flip.
Dependent EventsTwo events are dependent if the outcome of the first event DOES affect the outcome of t...
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Core Formulas
Probability of Two Independent Events
$P(A \text{ and } B) = P(A) \times P(B)$
To find the probability that two independent events, A and B, both happen, multiply the probability of event A by the probability of event B.
Probability of Two Dependent Events
$P(A \text{ and } B) = P(A) \times P(B \text{ after A})$
To find the probability that two dependent events, A and B, both happen, multiply the probability of event A by the probability of event B happening *after* event A has already occurred and changed the conditions.
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Challenging
A bag contains only red and blue marbles. There are 6 red marbles. If the probability of drawing two red marbles in a row *without replacement* is 1/3, how many total marbles were in the bag initially?
A.9
B.10
C.12
D.15
Challenging
A weather forecast states there is a 50% chance of rain on Saturday and a 50% chance of rain on Sunday. A student multiplies 0.5 by 0.5 to find a 25% chance of rain on both days. This calculation is only correct if...
A.the weather on Saturday is dependent on the weather on Sunday.
B.it is guaranteed to rain on one of the days.
C.the student used the wrong formula.
D.the weather on Saturday and the weather on Sunday are independent events.
Challenging
A small deck has 5 red cards and 5 black cards (10 total). You draw two cards without replacement. What is the probability that the two cards are of *different* colors?
A.25/90
B.50/90
C.20/100
D.50/100
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