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David and Connor O'Leary didn't think they would be chosen to compete on "The Amazing Race."

Oh, the Utahns applied. And they're the kind of people the casting directors on the CBS reality/competition show seem to search out. David, 58, and his son, Connor, 22, are bright, attractive, athletic — and they're both cancer survivors. (David had prostate cancer; Connor had testicular cancer.)

Still, when the call came, they were "dumbfounded," said David O'Leary, who works in investment properties. "I thought we had 0 percent chance of getting on."

It was the younger O'Leary, a professional bicycle racer, who suggested applying. "I love the show," Connor O'Leary said. "Going to awesome places. Great adventures. I remember thinking, 'My dad and I would be so great at that.' "

His father agreed to apply, although, "Honestly, I didn't think he'd follow through with it," said David O'Leary, sounding just like a dad.

They made their video, sent it off and pretty much forgot about it. Until they were contacted early last fall while Connor O'Leary was racing in Europe and his parents were there to watch him.

Both O'Learys leapt at the chance to be contestants on "The Amazing Race" (Sunday, 7 p.m., CBS/Channel 2), which was filmed in November-December 2012. Two-person teams race around the world, tackle challenges, try to avoid finishing last (and being eliminated) each week — and compete to win the race and the $1 million prize.

The money wasn't so much on the O'Learys' minds. "If someone came to you and said, 'You can go around the world and do all these thrilling things with your son,' would you say no?" David O'Leary said. "I'm thinking, 'How much do I have to pay?' "

They did their best to prepare, watching previous seasons of the show over and over and plotting out strategies.

"But in reality, nothing can prepare you," David O'Leary said. "Once the adrenaline starts flowing, all bets are off."

Connor O'Leary added: "I think your true colors show."

Under the pressure of competition, more than one racer has come out of this show looking less than amazing. But David O'Leary said he kept his wife's warning in mind — "Don't embarrass the family."

And both O'Learys said they had such a great time they'd love to do it again.

"It was an amazing, amazing experience with my dad," Connor O'Leary said. "One that I wouldn't trade for the world."

"We had so much fun," his father said. "Connor is great in stressful situations. He is not only an incredible athlete, he's bright. He's the whole package. I couldn't have had a better teammate."

Scott D. Pierce covers television for The Salt Lake Tribune. Email him at spierce@sltrib.com; follow him on Twitter @ScottDPierce.