Question

Question 2 [4 Marks]

Consider the following subsets of 𝑆 = {1, 2, 3, … ,8,9}:

(𝑖) [{1,3,5},{2,4,6,8},{5,7,9}]

(𝑖𝑖) [{1,3,5},{2,4,6,8},{7,9}]

Does 𝑖 and 𝑖𝑖 form a partition on sample space �

Answer 1

Partition of sample space

Let S be the sample space and $E_{1}, E_{2}, E_{3} \ldots E_{n}$ be Subset of S.

These events will induce partition of S if

i) $E_{i} \cap E_{j}=\phi$ (means number of common element between two subsets)

ii) $E_{1} \cup E_{2} \cup \ldots E_{\eta}=S$

Now

element of subset (i) and (ii) have common element $\{1,3,5\},\{2,4,6,8\}$ so, this is not partition on sample space S.