How to complete a Level 9 exam probability question and earn full marks; unconditional probability.

For this Level 9 examination question the video gives more detail than is needed for the full marks, but it does give credit to alternative methods.

The easiest way to work out the probabilities is by using sequences. Using a tree diagram is not advised the size required would be difficult to draw freehand and therefore prone to errors. A tree diagram is used at the start of the video only as part of the explanation of the method.

The calculations in the video make use of indices and decimals, it is expected that a calculator be available throughout.

To answer part (b) at first you might realise that there are other outcomes over the four days other than those mentioned, such as a combination of 2 wet and 2 dry days, and therefore you rightly assume that JJ is not correct, but if you do not support this statement with evidence you will earn no marks. Whether you choose to work out the probability for ‘2 wet and 2 dry days’ or ‘3 or more wet days’ with an explanation to substantiate your statement that ‘JJ is not correct’, you will earn full marks provided any calculations are completely correct.

The simplest and safest approach is to work out the probability for ‘3 or more wet days’, this is because there will be the same number of combinations for the ‘3 or more dry days’ and therefore easier to write out the sequences.

If you had decided to work out the combinations of ‘2 wet and 2 dry days’, for which there are a different number of combinations, then you would need to subtract the sum of the two probabilities obtained from 1 in order to find the probability for ‘3 or more wet days’

You might decide to calculate the probabilities for all three events in order to provide a check; which if correct would total to 1.

All these points are demonstrated in the video.

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