Probability measures how likely an event is on a scale from 0 to 1. SAT questions may use equally likely outcomes, two-way tables, repeated selections, or conditional language such as ‘given that.’
Essential concepts
\[P(A)= rac{ ext{favorable outcomes}}{ ext{total outcomes}} qquad P(A^c)=1-P(A)\]
The complement rule is often faster when ‘at least one’ is easier to handle as one minus ‘none.’
SAT strategy and application
Calculate a simple probability
A bag contains 3 red and 5 blue tokens. One token is selected at random. What is the probability it is red?
- Count favorable outcomes
There are 3 red tokens.
- Count total outcomes
\(3+5=8\) tokens.
Probability: \( rac{3}{8}\).
Mistakes and traps
Check your understanding
A jar contains 4 green and 6 yellow beads. What is the probability of selecting a green bead?
- \( rac{2}{5}\)
- \( rac{3}{5}\)
- \( rac{2}{3}\)
- \( rac{4}{6}\)
Show answer and explanation
Answer: \( rac{2}{5}\)
\(4/(4+6)=4/10=2/5\).
Key takeaways
What to remember
- Define the relevant sample space before choosing a denominator.
- Translate ‘and,’ ‘or,’ ‘given,’ and ‘at least one’ carefully.
- Update probabilities for selections without replacement.
- Use complements when the opposite event is simpler to calculate.
Continue learning
Put these notes into practice
Apply the ideas with SAT-style questions, then reinforce key details with flashcards.