“We had a really hard time casting the role, and in retrospect it was obvious that the problem was not the actresses but the conception of the character,” he said. Focus groups that watched the original pilot were left with protective feelings for the two naïve, socially awkward scientists, and they did not like the prospect of a bitter, manipulative woman taking advantage of them.

Image Two big brains and the evolving girl next door: from left, Johnny Galecki, Kaley Cuoco and Jim Parsons in The Big Bang Theory, a CBS comedy. Credit... Cliff Lipson/CBS

“What we all liked was the relationship between these two guys, one who wants his world to be bigger and the other who wants his world to be smaller,” Mr. Prady said. “I think that’s what everyone looked at and said, ‘This is worth trying again.’ ” The creators decided to keep the male characters and to persuade Mr. Parsons and Mr. Galecki not to take another series in the year between the two pilots.

They also called back one of the actresses who auditioned unsuccessfully for the original female role: Kaley Cuoco, a former child actor who played opposite John Ritter in the comedy “8 Simple Rules for Dating My Teenage Daughter.” Much of the edge was taken off the character of Penny  so much that at first she looked to be little more than a jiggly blonde next door with no apparent motivation for being interested in two science geeks.

It took awhile to find the character’s voice, but now Penny “is one of the guys,” Ms. Cuoco said. “She’s not some untouchable creature.”

Over the first two seasons Penny and Leonard edged toward each other and are now in a full-fledged relationship. But theirs is not the unbelievable type of couple  a gorgeous female and a paunchy, slacker male  that has been so popular in Judd Apatow films recently.

“Penny has been in horrible relationships and picked the wrong guy constantly,” Ms. Cuoco said. “I think she has more baggage than the guys.”