CLASS 10 · LEARNING KNOWLEDGE
Tree diagrams and conditional probability
How it works
Conditional probability considers only cases that satisfy an additional condition. A tree diagram helps distinguish between drawing with and without replacement. Disjoint paths of an event are added.
Note
P(A|B) = P(A ∩ B) / P(B) for P(B) > 0; without replacement, numerator and denominator change.
P(A|B) = P(A ∩ B) / P(B) for P(B) > 0; without replacement, numerator and denominator change.
An example
A bag contains 6 red and 6 blue balls. Two draws are made without replacement. What is P(exactly one red) in percent? Round to two decimal places. Give the result in %.
Two paths: Red–Blue and Blue–Red. P=6/12·6/11+6/12·6/11. Result: 54.55 %.
Try it yourself now
50 Exercises · three difficulty levels · selection and number input
To the learning unit →Own explanation and own practice exercises by AmyMath. Subject reference framework: KMK Educational Standards Mathematics ESA/MSA. The topic assignment may vary by federal state.