Combined Probability

Combined Probability is the result of two probabilities contributing to a single probability. For example, you might say the probability of flipping 2 heads in a row is $1/4$.

Example

There is a d12 die on the table, Ronald gives it a throw. He needs to roll both a 3, and a 6 on a second roll. Should he do this, he will have £600 in his wallet. What is the probability Ronald pulls it off?

$$\begin{align} chance\;of\;rolling\;a\;3 & = \frac{1}{12} \\ chance\;of\;rolling\;a\;6 & = \frac{1}{12} \\ combined\;probability & = \frac{1}{144} \end{align}$$

What is the probability that Ronald doesn't win £600?

$$\begin{align} combined\;probability & = \frac{1}{144} \\ probability & = 1 - \frac{1}{144} \\ & = \frac{143}{144} \end{align}$$

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