Conditional probability: tree diagrams and the formula

Sample Conditional probability: tree diagrams and the formula questions

A few of the 16 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 12 marksGrade 6-7
   A jar contains 6 black marbles and 7 white marbles (13 marbles in total). Sam takes a marble at random and does not put it back, then takes a second marble at random. Given that the 1st marble taken was black, work out the probability that the 2nd marble is also black. Give your answer as a fraction in its simplest form.
   Show the worked solution

   We are told the 1st marble was black and NOT replaced, so on the 2nd draw there are only 5 black marbles left, out of 12 marbles total (one fewer than the original 13, since one has been removed). M1

   Reading this branch of the tree directly: P(2nd is black given 1st is black) = $\dfrac{5}{12} = 5/12$

What are the common mistakes in Conditional probability: tree diagrams and the formula?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

• Forgets that the total (denominator) also decreases after an item is removed without replacement

  Leo used the ORIGINAL total (10) and original green count (4), but since the first counter is NOT replaced, both the number of green counters AND the total must be reduced by 1 for the second draw

• Uses the same probability for a second draw without replacement, forgetting it has changed

  Forgets that removing the first red counter changes the composition of the bag, and reuses the original probability of 3/12 = 1/4 for the second draw instead of correctly using 2 red counters out of 11 remaining, i.e. 2/11.

• Adds the individual probabilities of an event happening on separate occasions instead of using the complement method, causing double-counting of overlapping outcomes.

  Adds the two individual probabilities of being late (0.15+0.15=0.3) instead of correctly using the complement method: 1 − P(not late on either day), which avoids double-counting the case where the train is late on both days.

Quick answers about Conditional probability: tree diagrams and the formula

How many Conditional probability: tree diagrams and the formula practice questions are there?

There are 16 self-marking GCSE Maths questions on Conditional probability: tree diagrams and the formula, written for AQA, Pearson, OCR across Higher tier. Each one is marked instantly and has a full worked solution.

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