To solve this problem, we need to understand the trend in the solubility of alkaline earth metal sulphates in water.$\\$The alkaline earth metals are: Mg, Ca, Sr, and Ba.$\\$The solubility of sulphates of these metals generally decreases as we move down the group in the periodic table.$\\$This is due to the increasing lattice energy of the sulphates compared to the hydration energy as the size of the metal cation increases.$\\$Let's analyze the solubility trend:$\\$• Magnesium sulphate (MgSO$_4$) is highly soluble in water.$\\$• Calcium sulphate (CaSO$_4$) is less soluble than magnesium sulphate.$\\$• Strontium sulphate (SrSO$_4$) is even less soluble.$\\$• Barium sulphate (BaSO$_4$) is the least soluble among them.$\\$Therefore, the correct order of decreasing solubility is:$\\$Mg > Ca > Sr > Ba$\\$This corresponds to Option 4.$\\$Thus, the correct answer is Option 4: Mg > Ca > Sr > Ba.