$P(x=4)$= _______

The probability of $P(X=4)$from the given table.

A corporation want to assess its attrition rate, or the length of time that new personnel stay with the organization. They've developed the following probability distribution over time.

Let us define $X$ be the number of years a new hire will stay with the company and $P\left(X\right)$the probability that a new hire will stay with the company $X$years.

Only when, according to discrete distribution features, is $P\left(X\right)$ said to be the probability mass function of a $X$ discrete variable.

i. $P\left(X\right)$$\ge$0 for all$X$
ii.localid="1648447521559" $\sum P\left(X\right)=1$

We may calculate the probability using condition (ii)$P(X=4)$as:

localid="1649438056252" $$\begin{gathered} \sum P\left(X\right)=0.12+0.18+0.30+0.15+P\left(X_4\right)+0.10+0.05=1 \\ P\left(X_4\right)=1-0.90=0.10 \end{gathered}$$

As a result, the probability is:

$P(x=4)=0.10$