Video: AQA GCSE Mathematics Higher Tier Pack 4 • Paper 3 • Question 9

In a bakery, there are 64 sweet pastries and 30 savoury pastries. The probability that a sweet pastry chosen at random contains milk is 7/8. The probability that a savoury pastry chosen at random contains milk is 1/6. a) Calculate the number of pastries in the bakery that contain milk. b) Calculate the probability that a randomly chosen pastry does not contain milk.

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Video Transcript

In a bakery, there are 64 sweet pastries and 30 savoury pastries. The probability that a sweet pastry chosen at random contains milk is seven-eighths. The probability that a savoury pastry chosen at random contains milk is one-sixth. Part a) Calculate the number of pastries in the bakery that contain milk. Part b) Calculate the probability that a randomly chosen pastry does not contain milk.

In part a) then, we’re asked to calculate the number of pastries in the bakery that contain milk. So we first need to work out the number of sweet pastries that contain milk and then the number of savoury pastries that contain milk. We’ll then add these numbers together to give the total number of pastries in the bakery that contain milk.

We’re told there are 64 sweet pastries in the bakery and the probability that if we choose one of these sweet pastries at random that it will contain milk is seven-eighths which means the number of sweet pastries that contain milk is seven-eighths of 64. There are different ways that we could work this out.

For example, we could remember that in maths, the word “of” usually means multiply. So to find seven-eighths of 64, we need to multiply seven-eighths by 64. We could do this by writing the integer 64 as the fraction 64 over one and then remembering our rules for multiplying fractions. Cross cancelling would help here.

Alternatively, we could first find one-eighth of 64 by dividing 64 by eight and then multiply it by seven in order to give seven-eighths. 64 divided by eight is eight. We should know that because that’s in our times tables. Eight times eight is 64 and seven times eight is 56. So this tells us that there are 56 sweet pastries which contain milk in the bakery.

For the savoury pastries, there are 30 of them. And we’re told that the probability that a randomly chosen savoury pastry contains milk is one-sixth which means that one-sixth of the savoury pastries contain milk. We, therefore, need to find one-sixth of 30 which we can do by dividing 30 by six and it gives five.

We found then that there are 56 sweet and five savoury pastries in the bakery which contain milk. The total number of pastries in the bakery which contain milk is the sum of 56 and five which is 61.

Now, let’s look at part b). We’re asked to calculate the probability that a randomly chosen pastry does not contain milk. If the pastry is chosen at random, then this means that every pastry in the bakery has an equal probability of being picked which means to find the probability that this pastry does not contain milk, we need to find the number of pastries in the bakery that do not contain milk and divide it by the total number of pastries in the bakery.

At the start of the question, we were told that there are 64 sweet and 30 savoury pastries in the bakery. So the total number of pastries is 64 plus 30 which is 94. We worked out in part a) of the question that the number of pastries in the bakery that do contain milk is 61. So to work out the number that do not contain milk, we need to subtract 61 from the total of 94, which gives 33.

We can then substitute these two numbers into the numerator and denominator of our fraction, giving 33 over 94. This fraction can’t be simplified as 33 and 94 have no common factors other than one. So we found that the probability that a randomly chosen pastry does not contain milk is 33 over 94.

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