A sample space consists of three outcomes, X, Y, and Z. Which of the following could be a legitimate assignment of probabilities to the outcomes?
A) $P ( X ) = 0.3 \quad P ( Y ) = 0.6 \quad P ( Z ) = 0.9$
B) $P ( X ) = 0.3 \quad P ( Y ) = 0.2 \quad P ( Z ) = 0.5$
C) $P ( X ) = 0.3 \quad P ( Y ) = 0.3 \quad P ( Z ) = 0.3$
D) $P ( X ) = 0.7 \quad P ( Y ) = - 0.3 \quad P ( Z ) = 0.6$

Question

Quizplus · Accepted Answer

The probabilities assigned to each outcome must be between 0 and 1, inclusive. Option A and D violate this condition. In option C, the sum of probabilities is not equal to 1. Hence, the only valid choice is B where the probabilities of all three outcomes are between 0 and 1 and sum up to 1.

A Sample Space Consists of Three Outcomes, X, Y, and Z