Question

4.1 empirical probability. apply the rules of probability. assume $p_0, p_1$, and $p_2$ are probabilities for simple events. is $p_0 = 0.92$ a valid probability? is $p_1 = 1.69$ a valid probability? is $p_2 = 0$ a valid probability? could $p_0 = 0.49, p_1 = 0.31, p_2 = 0.2$ be a valid probability assignment? could $p_0 = 0.31, p_1 = 0.74, p_2 = 0.1$ be a valid probability assignment? question help: message instructor

Explanation:

Step1: Recall probability rules

A probability of an event $P$ must satisfy $0\leq P\leq1$.

Step2: Check $P_0 = 0.92$

Since $0\leq0.92\leq1$, it is a valid probability.

Step3: Check $P_1 = 1.69$

Since $1.69>1$, it is not a valid probability.

Step4: Check $P_2 = 0$

Since $0$ satisfies $0\leq0\leq1$, it is a valid probability.

Step5: Check $P_0 = 0.49, P_1 = 0.31, P_2 = 0.2$

$P_0 + P_1+P_2=0.49 + 0.31+0.2=1$, and each individual probability is between $0$ and $1$, so it is a valid probability - assignment.

Step6: Check $P_0 = 0.31, P_1 = 0.74, P_2 = 0.1$

$P_0 + P_1+P_2=0.31 + 0.74+0.1 = 1.15>1$, so it is not a valid probability - assignment.

Answer:

Is $P_0 = 0.92$ a valid probability? yes
Is $P_1 = 1.69$ a valid probability? no
Is $P_2 = 0$ a valid probability? yes
Could $P_0 = 0.49, P_1 = 0.31, P_2 = 0.2$ be a valid probability assignment? yes
Could $P_0 = 0.31, P_1 = 0.74, P_2 = 0.1$ be a valid probability assignment? no