Question

a decision maker subjectively assigned the following probabilities to the four outcomes of an experiment: $p(e_1)=0.10, p(e_2)=0.15, p(e_3)=0.40$, and $p(e_4)=0.20$. are these probability assignments valid? explain.

Explanation:

Step1: Recall probability rules

For a set of probabilities of all possible outcomes of an experiment, they must satisfy two conditions: 1. Each probability $P(E_i)\geq0$. 2. $\sum_{i}P(E_i) = 1$.

Step2: Check non - negativity

We have $P(E_1)=0.10\geq0$, $P(E_2)=0.15\geq0$, $P(E_3)=0.40\geq0$, $P(E_4)=0.20\geq0$. All probabilities are non - negative.

Step3: Calculate the sum

$P(E_1)+P(E_2)+P(E_3)+P(E_4)=0.10 + 0.15+0.40 + 0.20$.
$=0.85
eq1$.

Answer:

No, because the sum of the probabilities of all possible outcomes ($0.85$) is not equal to 1.