Former California governor Ronald Reagan strengthened his lead in Florida presidential preference caucus balloting yesterday, winning more than a third of the randomly selected delegates in the state's second largest Republican county.

In the last major county caucus before the Nov. 17 state convention in Orlando, Broward County Republicans picked a delegation that reflects the lingering strength of the organization Reagan built during the 1976 campaign.

Delegates to the Orlando convention will participate in a presidential straw ballot, but the balloting will have little significance beyond demonstrating the early organizational abilities of the candidates. Delegates to the national nominating convention will be chosen in a March primary.

Of Broward County's 157 delegates, 123 were chosen at random from about 1,200 application cards placed in a lottery drum.

Most of the candidates' campaign efforts were directed at getting potential supporters to submit cards.

Of the delegates whose names were drawn from the drum, 42 were Reagan supporters, 21 for Connally, 12 for former Republican national chairman George Bush, 11 for Tennessee Sen. Howard Baker, six for South Dakota Sen. Larry Pressler and five for Illinois Rep. Philip M. Crane. Twenty-two delegates were undecided and five could not be reached.