Conditional probability
Chances that change once you know something.
Pen and paper is fine · no calculator needed why?
Opens at level 29.
Lesson and untimed practice
Read the full lesson and try each skill without a clock. About 3 minutes to read.
skills · practice stats
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From a table not tried yet
worked example
Of 241 customers, 14 bought online and returned something, 37 bought online and returned nothing, 72 bought in store and returned something, and 118 bought in store and returned nothing. What is the probability a customer returned something, given they bought online? Give the answer as a fraction in lowest terms.
Answer: 14/51
- Only look at the customers who bought online: 14 + 37 = 51.
- Of those, 14 returned something: 14/51.
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Two-stage chance not tried yet
worked example
You pick Box A with probability 1/3 and Box B with probability 2/3, then draw one ball at random from that box. Box A holds 3 white balls and 5 yellow balls; Box B holds 5 white balls and 1 yellow ball. What is the probability the ball is white? Give the answer as a fraction in lowest terms.
Answer: 49/72
- Weight each box’s chance of white by the chance of picking that box:
- 1/3 × 3/8 + 2/3 × 5/6 = 1/8 + 5/9
- = 9/72 + 40/72 = 49/72.
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Test results (Bayes) not tried yet
worked example
1% of transactions are fraudulent. A filter flags 95% of fraudulent transactions, and also wrongly flags 5% of legitimate ones. A transaction is flagged. What is the probability it is fraudulent? Give the answer as a fraction in lowest terms.
Answer: 19/118
- Picture 10,000 transactions: 100 are fraudulent, and 95 of them are flagged.
- Of the 9,900 legitimate ones, 495 are flagged.
- So 95 of the 590 flagged transactions are fraudulent: 95/590 = 19/118.
rest ladder
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