Replace word in <p> in <div> using jquery

You need to target the p tag inside the #notice:

$("#notice p").text(function(i, text) {
    return text.replace("some", "My");
});

---

Update 2020-03

This same logic can now be made even simpler by using an arrow function:

$('#notice p').text((i, t) => t.replace('some', 'My'));

This will work in any browser except Internet Explorer.

Read http://api.jquery.com/text/#text-functionindex--text

$("#notice p").text(function (_, ctx) {
    return ctx.replace("some", "My");
});

or

$("#notice p").text($("#notice p").text().replace("some", "My"));

or

var  p_tag = $("#notice p");
p_tag.text(p_tag.text().replace("some", "My"));

This is an overkill but anyway:

function replaceNodeText() {
    if (this.nodeType === 3) {
        this.nodeValue = this.nodeValue.replace(replaceNodeText.find, replaceNodeText.replace);
    } else {
        $(this).contents().each(replaceNodeText);
    }
}
replaceNodeText.find = "some";
replaceNodeText.replace = "my";
$("#notice").contents().each(replaceNodeText);

This function will preserve any html present inside the specified element. For example it will work on this HTML:

<div id="notice" class="box generalbox">
    <p>This is<br>some text.</p>
    <p>This is so<br>me text.</p>
    <p>This is <b>some</b> text.</p>
</div>

And produce the following output:

<div id="notice" class="box generalbox">
    <p>This is<br>my text.</p>
    <p>This is so<br>me text.</p>
    <p>This is <b>my</b> text.</p>
</div>

Demo here