“I’ll pick a woman to be vice president,” Joe Biden announced during his Democratic presidential primary debate last week against Bernie Sanders. “There are a number of women who are qualified to be president tomorrow.”

That’s true. It’s been true for decades. Most recently, Hillary Clinton filled that bill in 2016. A woman elected to serve in the White House is overdue.

There is a cliché about the vice president being one heartbeat away from becoming the commander in chief. Because of Biden’s age, that trope takes on added significance.

With three more state primary victories Tuesday, Biden appears the certain Democratic nominee. And if Biden wins in November, he will be 78 years old; the oldest person ever to occupy the White House. He will be eight years older than Donald Trump was in 2017, when Trump became the oldest president to assume office.

It doesn’t take much to imagine Biden a one-term president. In that case his choice for vice president would almost certainly be a front-runner for the Democratic nomination in 2024.

There have been two previous major-party female vice-presidential candidates. In both cases the tickets lost. Walter Mondale chose Geraldine Ferraro in a quixotic mission to unseat Ronald Reagan in 1984. John McCain chose Sarah Palin in his unsuccessful run against Barack Obama in 2008.

Biden is leading in early polls to defeat the unpopular and incompetent Trump in November. The odds this time are better than even that a woman could be one heartbeat away from president.

Biden’s pledge to name a woman is smart politics. His path to the White House hinges on the female vote.

Women compose the largest voting bloc in the Democratic coalition. They are the majority of the Democratic Party. Females constitute 56 percent of all the votes counted through last week in the Democratic presidential primary contests, according to a Washington Post exit poll survey. Women vote at higher percentage rates than men.

In 2018, women put the Democrats in control of the House of Representatives. Almost 60 percent of the votes cast by all women in 2018 went to House Democratic candidates.

There now are more women serving in the House than ever before. Of those 101 female House members, 88 are Democrats, including House Speaker Nancy Pelosi. Of the 26 female senators, 17 are Democrats.

So, let’s give Biden credit for having a firm grasp of the politically obvious in making an early announcement about a female running mate.

But let’s also express chagrin at the way Biden made his declaration. By announcing a nameless running mate based on gender, leaving her qualifications for another day, Biden gave his opponents an opening to brand the woman he chooses as an affirmative-action sop.

Biden inadvertently put his future running mate at a disadvantage by advancing her sex over her competence.

Biden could have avoided the brickbats if he had answered that debate question by prioritizing the qualities he seeks in a vice president. Then, he could have said he intends to find the woman with the bona fides to meet those qualifications.

Fortunately, as Biden acknowledged in Sunday’s debate, Democrats have an abundance of qualified women from whom to choose. Among the top choices from the Senate are three who ran against Biden for the nomination: Elizabeth Warren (Massachusetts), Amy Klobuchar (Minnesota), and Kamala Harris (California).

There are six Democratic women governors. The two female governors most prominently mentioned are Gina Raimondo of Rhode Island and Gretchen Whitmer of Michigan. Stacey Abrams, a former Georgia state senator who ran for governor in 2018, and who has made a strong case that voter suppression caused her narrow defeat, is mentioned as a possibility.

A female as a senior elected official serving inside the White House is long overdue. A wise choice for running mate will only enhance Biden’s chances of beating Trump and restoring a measure of confidence in government to Washington.