Correlation between categorical variables based on the target distribution
Your answer is $\chi^2$ (chi-squared) test of independence.

First we have to calculate the expected value of the two nominal variables.  We can calculate the expected value of the two nominal variables by using this formula:

$E_{i,j} = \frac{\sum_{k=1}^cO_{ik}*\sum_{k=1}^rO_{kj}}{N}$

Where,

$E_{ij}$ = Expected value of the cell $i$, $j$

$\sum_{j=1}^cO_{ij}$ = Sum of the ith column

$\sum_{k=1}^rO_{kj}$ = Sum of the kth row

$N$ = total number

After calculating the expected value, we will apply the following formula to calculate the value of the Chi-Square test of Independence:

$\chi^2 = \sum\sum\frac{(O_{ij}-E_{ij})^2}{E_{ij}} $: Chi-Square test of Independence

$O_{ij}$ = Observed value of two nominal variables

$E_{ij}$ = Expected value of two nominal variables

Degree of freedom is calculated by using the following formula:
$df = (r-1)(c-1)$

Where,
DF = Degrees of freedom
r = number of rows
c = number of columns

Hypothesis:

Null hypothesis: Assumes that there is no association between the two variables.

Alternative hypothesis: Assumes that there is an association between the two variables.

Hypothesis testing: Hypothesis testing for the chi-square test of independence as it is for other tests like ANOVA, where a test statistic is computed and compared to a critical value.  The critical value for the chi-square statistic is determined by the level of significance (typically .05) and the degrees of freedom.  The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) where r is the number of rows and c is the number of columns. If the observed chi-square test statistic is greater than the critical value, the null hypothesis can be rejected.