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 two events, we need to multiply their individual probabilities.
In this case, we are looking for the intersection of events {O3} and {O5}. It means we want to find the probability that both event O3 and event O5 occur.
Given the probabilities of each outcome:
w1 = 0.15,
w2 = 0.25,
w3 = 0.10,
w4 = 0.20,
w5 = 0.15,
w6 = 0.15,
The probability of event {O3} occurring is denoted as P(O3) and is equal to w3, which is 0.10.
The probability of event {O5} occurring is denoted as P(O5) and is equal to w5, which is 0.15.
To find the probability of the intersection {O3} ∩ {O5}, we can multiply the probabilities:
P({O3} ∩ {O5}) = P(O3) * P(O5) = 0.10 * 0.15 = 0.015.
Therefore, the probability of the intersection {O3} ∩ {O5} is 0.015 or 1.5%.