In order to build a full joint probability table for a case in which there are three binary random variables, say Val1, Val2 and Val3, 5000 experiments have been conducted. If an event with Val1=False, Val2=False and Val3=False appeared 601 times in the experiments, the probability of this event is (as %, keep 2 decimal places).

Question

In order to build a full joint probability table for a case in which there are three binary random variables, say Val1, Val2 and Val3, 5000 experiments have been conducted. If an event with Val1=False, Val2=False and Val3=False appeared 601 times in the experiments, the probability of this event is  (as %, keep 2 decimal places).

BlackTom AI · Accepted Answer

We start by identifying the given data: there were 5000 experiments in total, and the event (Val1=False, Val2=False, Val3=False) occurred 601 times.
To find the probability of this event, we use the basic empirical probability formula: P(event) = (number of favorable outcomes) / (total number of trials).
Here, that is P = 601 / 5000.
Compute the fraction: 601 ÷ 5000 = 0.1202.
To express this as a percentage, multiply by 100: 0.1202 × 100 = 12.02%.
Since the instruction asks to keep two decimal places, we present the final probability as 12.02%.
Note: If one were to round differently or miscount the total trials (denominator), the result would deviate. For example, using 601/6000 would give 10.02%, which is incorrect given the denominator is 5000. Similarly, forgetting to convert to a percentage would yield 0.1202 as a decimal rather than 12.02%.

42172 Introduction to Artificial Intelligence - Spring 2025 Lec11 class quiz

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