JSFiddle - React, Tailwind, and code Playground

HTML

<label for="petType">Type of Pet:</label>Cat
<input class="radio" name="petType" type="radio" id="petType" value="cat">Dog
<input class="radio" name="petType" id="petType" type="radio" value="dog">Other
<input class="radio" name="petType" id="petType" type="radio" value="other">
<label for="state">Breed:</label>
<select id="breed">
    <option>Shiba Inus</option>
    <option>Pembroke Welsh Corgi</option>
    <option>Boxer</option>
    <option>English Bulldog</option>
</select>

CSS

#breed {
    display:none;
}

JavaScript

function asdf(x) {
     var breed = document.getElementById('breed');
     if (this.value == "dog") {
         breed.style.display = "inline";

     } else {
         breed.style.display = "none";
     }
 }

 var typeOfPet = document.getElementsByName('petType');
 for (var i = 0, l = typeOfPet.length; i < l; i++) {
     typeOfPet[i].addEventListener('change', asdf, false);
 }