Solutions - 5010-01

(a)

(1) Count outcomes:

Since there are 6 possible results of rolling a die and $2$ possible results of a coin flip, the sample space has $6\cdot 2=12$ elements.

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(2) Describe the sample space $\mathrm{\Omega }$ using set builder notation:

$$\mathrm{\Omega }=\{(i,j):i\in \{1,\dots ,6\},j\in \{H,T\}\}$$

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(b)

The number of events equals the number of subsets of $\mathrm{\Omega }$, i.e. $|𝒫(\mathrm{\Omega })|$.

$$|𝒫(\mathrm{\Omega })|=2^{|\mathrm{\Omega }|}=2^{12}=4096$$