A LITTLE LIGHTBULB MOMENT
Quantitative reasoning: probability, statistics and word problems
Independent Events
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Two flips keep their own odds.
The idea behind the cue
Independent events do not affect each other’s probabilities. For independent A and B, P(A and B)=P(A)×P(B). Independence is a relationship, not just two events happening together.
Practice this flashcard →Make it memorable
Short & simple
Two flips keep their own odds.
Acronym
IM — Impatient Muffins.
Story
A coin flips in a windy hallway and then again outside. The first flip cannot whisper to the second. Each flip keeps its own odds, like two separate lottery tickets.
Connect the pieces
- I (Impatient) → Independent: One event does not change the probability of the other.
- M (Muffins) → Multiply: For independent events, multiply the probabilities: P(A and B)=P(A)×P(B).
- Impatient · Independent: One event does not change the probability of the other.
- Muffins · Multiply: For independent events, multiply the probabilities: P(A and B)=P(A)×P(B).
Know the limits
Do not assume independence when one event changes the pool for the next, such as drawing without replacement.
Further reading · OpenStax science and mathematics textbooks ↗Check your understanding
A fair coin is flipped twice. What is the probability of getting heads both times?
A. 1/2
B. 1/4
C. 1/8
D. 1
Reveal explanation
1/4
The flips are independent, so multiply: 1/2 × 1/2 = 1/4.