Dependent events without replacement

Sample Dependent events without replacement questions

A few of the 42 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

1. Question 13 marksGrade 6
   There are 9 counters in a bag: 7 green counters and 2 blue counters. Ria takes at random two counters from the bag (without replacement). Work out the probability that Ria takes one counter of each colour.
   Show the worked solution

   P(green then blue) = 7/9 × 2/8 = 14/72. M1

   P(blue then green) = 2/9 × 7/8 = 14/72. M2

   P(one of each colour) = 14/72 + 14/72 = 28/72 = 7/18. A1
2. Question 24 marksGrade 6-7
   A bag contains 3 red counters and 5 blue counters (8 counters in total). Jodie takes a counter at random and does not put it back. Jodie then takes a second counter at random from the bag. Work out the probability that one counter of each colour is taken (one red and one blue, in either order). Give your answer as a fraction in its simplest form.
   Show the worked solution

   Because the counter is NOT replaced, the denominator on the second pick is 7, not 8.

What are the common mistakes in Dependent events without replacement?

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.

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

  Treats the second draw as independent of the first (as if with replacement), squaring the first probability k/(k+1) to get k²/(k+1)² instead of correctly reducing both counts for the second draw to get (k-1)/(k+1).

• Counts only one ordering of a combined event when multiple valid orderings should be added

  Only calculated one of the 3 possible orderings of "two black, one grey" and forgot to add the other two.

• Calculates the probability of all matching outcomes instead of exactly the number specified

  Calculated P(all three black) instead of P(exactly two black and one grey).

Quick answers about Dependent events without replacement

How many Dependent events without replacement practice questions are there?

There are 42 self-marking GCSE and IGCSE Maths questions on Dependent events without replacement, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Higher and Extended tier. Each one is marked instantly and has a full worked solution.

Do I need an account to practise Dependent events without replacement?

No. You can start practising Dependent events without replacement straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.