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Math / Statistics / Grade 9 / mt901

Use Conditional Probabilities

Change the denominator when the condition changes.

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Learn the skill

For a conditional probability, restrict attention to the group named after 'given.' Count favorable outcomes within that group, then divide by that group's total. Do not automatically use the total sample size.

Worked example

If 3 of 5 blue tiles are round, the probability of round given blue is 3/5, even if a box contains many other colors.

An Invented Tile Box

Red round: 6. Red square: 2. Blue round: 4. Blue square: 8. Select one tile uniformly at random from the stated group.

1. What is the probability of red given round?
2. What is the probability of round given red?
3. How many tiles are in the whole box?
4. What is the probability of blue given square?
5. Why can P(red given round) differ from P(round given red)?