Question

a single die was rolled 100 times. the possible outcomes for the random variable x are shown below with their possible probabilities. find the missing probability

Explanation:

Step1: Recall the property of probability distribution

The sum of all probabilities in a probability distribution is \(1\). Let the missing probability be \(p\). Then \(0.23 + 0.11+0.09 + 0.22+p + 0.1=1\).

Step2: Simplify the left - hand side of the equation

First, add the known probabilities: \(0.23+0.11 = 0.34\), \(0.34+0.09=0.43\), \(0.43 + 0.22=0.65\), \(0.65+0.1 = 0.75\). So the equation becomes \(0.75 + p=1\).

Step3: Solve for \(p\)

Subtract \(0.75\) from both sides of the equation: \(p=1 - 0.75\).

Answer:

\(0.25\)