When it comes to solving probability problems in GCSE Maths it's important to know the differences between independent and dependent events, becuase these effect the probability outcome. 

If two events are independent, then the outcome of one event have no effect on the outcome of the second. For example, if I flip a coin twice, whether the first toss landed heads or tails has no impact on how the second toss landed. The probability of getting heads first time was ½, and the probability of getting heads the second time was still ½.

These types of question are best solved using a probability tree diagram.

In order to solve probability problems using a tree diagram, we need to know that we multiply along the branches (for AND) and add vertically ( for OR).


A bag contains 4 red balls, 6 black balls. A ball is taken out of the bag at random and then replaced. Then another ball is taken out and then replaced.

To find out the probability that a black ball, then a red ball, can be done by multiplying the probability of getting a black ball (3/5) by the probability of getting a red ball (2/5) so the probability of getting a black ball then red ball is 3/5 x 2/5 = 6/25 

To find the probability of getting a ball with each colour i.e. what is the probability of getting first a black then a red ball, and the probability of getting a red then a black ball. From our diagram we can see the probability of both is 6/25. So we need to add these to get 12/25


Now, let's see if you can solve some probability problems with independent events, just click on 'Test Questions'

Or you can Ask a Question online, and get help from the community. 



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AQA Unit 1 March 2011 (F) - Page 4, Question 2

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