Conditional Probability Worksheet

Conditional probability at a glance

Conditional probability is the probability of an event occurring given another event has already occurred. When finding probability based on a condition, we need to consider what has occurred before. For example, if we have a bag containing 3 red marbles and 2 blue marbles, the probability of picking a red marble is 0.6, and the probability of picking a blue marble is 0.2. If we pick one marble out then these values change. If a red marble is picked (and not replaced) there would then be 2 red marbles and 2 blue marbles left. The probability of picking a red marble would now be 0.5 and a blue marble would be 0.5.

Conditional probability problems often involve calculating the probability of two or more combined events. For example, 20 students put their name into a hat. The same student cannot be picked twice. The probability of picking the first student at random (event A) is 1 out of 20. Their name is removed from the hat so they cannot be picked again. The probability of picking a second student at random (event B) is 1 out of 19, as there are 19 student names remaining in the hat. Event B is conditional on the outcome of event A because the total number of outcomes change between the two events. 

It is useful to draw a tree diagram when calculating conditional probabilities.

We may be required to extract information from a two way table or Venn diagram given certain conditions in order to solve a problem.

Looking forward, students can then progress to additional probability worksheets, for example the mutually exclusive events worksheet, the product rule for counting worksheet, or the probability tree diagrams worksheet.

For more teaching and learning support on probability our GCSE maths lessons provide step by step support for all GCSE maths concepts.