When it became clear to Johnson that he could not reach the top of the ticket, he began to consider the second spot. He had his staff look up how many presidents in the previous hundred years had died in office--five out of eighteen, giving him a better than 20 percent chance of reaching the presidency that way. When Clare Boothe Luce later asked him why he would accept the nomination to be number two, he answered: "Clare, I looked it up: one out of every four Presidents has died in office. I'm a gamblin' man, darlin', and this is the only chance I got." He said much the same thing to trusted journalists. So it was clear why Johnson would run with the "sickly" John Kennedy. He knew about the ailments that could threaten his life.
Of course, I'm exaggerating greatly in calling this "numeracy." Extrapolating from a sample size of 18 is problematic. Interestingly, though, more than double the sample size, as this article in the Concise Encyclopedia does, and you get similar numbers. As Table 2, shows, Annual Fatalities per 100,000 Persons at Risk for Presidents are 3,700. Over 4 years, that's about 15,000, or odds of 15 percent, close to LBJ's number.