Assume that your sample space is S = {O1, O2, O3, O4, O5, O6 } with associated weights (probabilities) w1 = 0.15, w2 = 0.25, w3 = 0.10, w4 = 0.20, w5 = 0.15, and w6 = 0.15. Determine the probability of the following events:

{O3 }∩{O5 }:

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To determine the probability of the intersection of events {O3} and {O5}, we need to multiply the probabilities of each individual event occurring.

Event {O3} has a probability of w3 = 0.10, while event {O5} has a probability of w5 = 0.15.

To find the probability of the intersection, we multiply these probabilities together:

P({O3} ∩ {O5}) = P({O3}) × P({O5}) = w3 × w5

Substituting the given values:
P({O3} ∩ {O5}) = 0.10 × 0.15 = 0.015

Therefore, the probability of the intersection of events {O3} and {O5} is 0.015.