1. P(H0|X) is very different from P(X|H0)

2. P(X|H0) – p-value (probability of observing the data, given null hypothesis is true
P(X|Ha) – (probability of observing the data, given alternative hypothesis is true
We, of course, have two more probabilities
P(H0) – probability null is true (and it can be very different, say, if we are looking for a sick person in a general population, it can be 1%
P(Ha) – suppose here we say alternative means not null, so it is 1-P(H0)

3. Bayes formula
We can easily see that probability null is true, given the data is P(H0|X)
Now, just plugging in several scenarios would show us that P(H0|X) is very different from P(X|H0)

4. Several scenarios Suppose P(X|H0)=0.05 and P(X|Ha)=0.80
Now, depending on the probability of H0 we would get very different results:
P(H0)
P(X)
P(H0|X)
0.5
0.43
0.06
0.9
0.13
0.36
0.99
0.86