From left, Randy Jackson, Mariah Carey, Keith Urban and Nicki Minaj are judges on Fox’s “American Idol.” (Todd Williamson/INVISION/AP)

After a half-hour spent cooling their heels and speculating which new diva was causing the delay of Fox’s “American Idol” Q&A session at Winter TV Press Tour 2013, critics finally got to ask Mariah Carey and Nicki Minaj whether the audition brawl leaked to TMZ in October was the real deal or a trumped-up gag to goose show ratings.

“We’re professionals. Have you ever had an argument with someone you’ve worked with?” said Minaj, dressed in a pretty beige, clingy dress and Louboutin heels so high she had to be walked to her seat onstage.

“This was sort of one-sided,” interjected Carey, her saintly smile hovering above a double strand of diamonds, above her equally clingy, strapless, emerald-green minidress.

“No, it wasn’t,” snapped Minaj.

One day after ABC News aired Babs Walters’s interview with Carey — in which she reiterated a claim she made in October about hiring a bodyguard to protect her from Minaj’s camp — Carey told TV critics: “The fighting is what it is. This is ‘American Idol.’ It’s bigger than . . . some stupid trumped-up thing” that was distracting from the singers and not fair to them.

Yet, interjected Minaj, every time she tries to talk about the contestants to reporters, they insist on pulling her back into conversation about the feud, the tape and TMZ.

Yeah — poor Nicki.

One critic asked each woman to say something nice about the other. While the crowd held their breath, Minaj began, calling Carey one of her favorite all-time artists and the shaper of a generation of singers.

Carey seemed to have more trouble talking about something other than herself but eventually got around to talking about working with Minaj on a single and realizing that Minaj was an artist who would go far. That single: “Up Out My Face.” Carey called the title “ironic.”

One critic wondered how they came to kiss and make up.

“I put on my sex tape,” Minaj responded.

“And, there it is,” Carey said, rolling her eyes.

The cacophony that ensued made it hard to understand what the two women were saying. Carey appeared to be talking about everyone being able to agree on the wonderfulness of her new shoes — also Louboutins, only strappier and not so high as Minaj’s and with little puffs at the toe.

Minaj, meanwhile, continued to discuss the merits of her sex tape as a peacekeeping device.

Finally, they appeared to run out of gas or at least remembered the media were in the room. Anyway, they stopped and caught their breath and let someone else on the panel speak.

Like exec producer Trish Kinane, who said they welcomed the vigorous (sometimes bodyguard-employing) give-and-take.

“We wanted judges who were experts and had a right to be here, and we also wanted honesty,” Kinane said, adding: “I think we’ve got it. They’re not shrinking violets — they say what they think, and we encourage that.”

Speaking of that, Minaj got asked about the trouble that rappers have had competing on “Idol.”

“I would never go on a show like this as a rapper,” she said. “I don’t think it’s authentic, and if you’re looking for people to believe you and see you as an authentic rapper, you wouldn’t do it.”

She noted that she “started off in the streets” and that this is as it should be for a hip-hop artist.

Guess what? Carey jumped in and said she, too, “never would have wanted to do this type of show — no offense to the show,” and that she started out sleeping on the floor of the studio. And that she owned only two dresses — one black and one pink.

TV’s latest serial killers

There have been more shows on TV that are more violent than Fox’s new serial-killer drama “The Following,” Fox Entertainment Chairman Kevin Reilly told TV critics Tuesday. “Clearly, he said, “there is an appetite — people like these things,”

The network has no plans to tinker with the eagerly anticipated stomach-churner in the wake of last month’s killing of 26 children and adults at Sandy Hook Elementary in Newtown, Conn., and other recent acts of real-life violence, Reilly told TV critics attending the press tour.

In the series from Kevin Williamson, Kevin Bacon stars as a former FBI agent brought back to track down a serial killer (James Purefoy) who has created a cult of killers around him.

In the first episode, a woman commits suicide by stabbing herself in the eye and piercing her skull with an ice pick; in another, a man is set on fire at a coffee stand.

Reilly noted last season’s No. 1-scripted TV series was the ghoulish AMC zombie drama, “The Walking Dead.”

“When you put on a thriller, you have to compete at that level. . . . We must match the intensity; otherwise, we’ll pale in comparison,” Reilly told critics, who’d asked him about the role of TV violence in the wake of the Sandy Hook tragedy.

“Before there was cable, Fox was cable,” Reilly waxed nostalgically, adding that it’s his goal, with such shows as “The Following,” to “get some of the Fox back in Fox.”

The new series, debuting Jan. 21, “adheres to broadcast standards,” Reilly said.

“If you put this [series] through the filter of broadcast standards, there’s nothing on that show we even had to fight over,” Reilly said. “I didn’t call [Fox’s Standards and Practices Department] and say, ‘Buckle up — this one’s pushing the boundaries.’ ”

Williamson said his new show is “not for the faint of heart.”

“It’s definitely — there’s some moments it’s squeamish,” he said. “You have to kind of look away. But it’s not the sum of the show.”

“There’s also drama and emotion and a lot of other things running through it. I take it episode by episode. . . . Some episodes, I find: Oh, wow, a lot of people died this week. Okay. So then when I sit down to write, no one dies the next week.”

Williamson said he and his writers were “traumatized” by the Sandy Hook shootings.

“So when I take pen to paper, there is a reaction to it and it sort of finds its way into what I do,” he said.

Asked how it will find its way into his work on the show, he answered: “I don’t know. We’ll find out. It just happened.”

It trivializes the issue to link the deaths at Sandy Hook to television — and to broadcast television, in particular — Reilly scolded, adding that “you can’t draw a direct linkage.”

“We have an FCC license and we take that seriously,” said Reilly, adding that Fox is open to an industrywide discussion about violent content.

But he said: “Everyone is looking for a scapegoat or wanting to put a finger on one thing that’s the problem. . . . We are just in an age of complex issues. It’s no one simple thing.”

Meanwhile, CBS, which has yet to make its presentations at the tour, should be steeling itself for questions.

Two days before Reilly spoke to the critics, NBC Entertainment Chairman Bob Greenblatt defended his new serial-killer drama, “Hannibal,” saying he thought that his other serial-killer drama, “Dexter” (Greenblatt used to head programming at Showtime) was not as violent as CBS’s “Criminal Minds.”

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