See also ‘Single Event Probabilities’

The probability of a ‘joint’ event – e.g. drawing a white ball followed by two black balls (from a jar containing 7 white and 5 black balls) can be calculated using total sample space.

Instead of calculating the individual probabilities of drawing a white ball – and then a black ball and then again a black ball, it is easier to just calculate the total number of outcomes (total Sample Space).

# of possible events (# ways in which the event can occur) / Total Sample Space  = probability

So – in our example – the total sample space = 12 balls – and three withdrawals – i.e. – 12 * 11 * 10 is the TOTAL number of ways to draw out three balls. This is part 1 of the calculation.
Now – total number of ways of drawing out 1 white ball (on the first try) – is 7. Total Number of ways of drawing out 2 black balls on the next two tries is 5 * 4.

However – these three draws can be interchanged – i.e. the first one can be black, the second white then the third black. So there’s THREE  permutations of the above that lead to the same result – 1 white and 2 black.

Therefore total number of ways these three balls can be drawn out = 3 * 7 * 5 * 4 = 420

Total Sample Space = 1320

Probability = 420/1320

Anuj holds professional certifications in Google Cloud, AWS as well as certifications in Docker and App Performance Tools such as New Relic. He specializes in Cloud Security, Data Encryption and Container Technologies.

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