Question

determine whether the statement is true or false. if the statement is false, make the necessary change(s) to produce a true statement. the sum of the probabilities of all possible outcomes in an experiment is 1. choose the correct answer below. a. this statement is false. to make this statement true, change \1\ to \4\. b. this statement is false. to make this statement true, change \1\ to \2\. c. this statement is false. to make this statement true, change \1\ to \3\. d. this statement is true.

Explanation:

In probability theory, one of the fundamental rules is that the sum of the probabilities of all mutually - exclusive and exhaustive (all possible) outcomes of an experiment must equal 1. For example, when flipping a fair coin, the probability of heads \(P(H)=\frac{1}{2}\) and the probability of tails \(P(T)=\frac{1}{2}\), and \(P(H)+P(T)=\frac{1}{2}+\frac{1}{2} = 1\). Another example is rolling a fair six - sided die. The probability of getting a 1 is \(P(1)=\frac{1}{6}\), for 2 is \(P(2)=\frac{1}{6}\), and so on. Then \(P(1)+P(2)+P(3)+P(4)+P(5)+P(6)=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=1\).

Answer:

D. This statement is true.