JSFiddle - React, Tailwind, and code Playground

HTML

<select id="meuSelect">
    <option value="a">Alfa</option>
    <option value="b">Beta</option>
    <option value="g">Gama</option>
</select>
<input type="text" />

JavaScript

var select = document.getElementById('meuSelect');
var input = document.querySelector('input');

select.addEventListener('change', function() {
    input.value = this.value;
	// se quiseres o texto usa 
	// var option = this.children[this.selectedIndex];
	// input.value = option.innerHTML;
});