The probability is not double. If p is the probability of a man under one bed, then (1-p) is the probability of no man under one bed, and (1-p)(1-p) is the probability of no man under either bed, and 1-(1-p)(1-p) is the probability of a man under either bed.
Although, this does approximate doubling for the vanishingly small probabilities we are talking about in Lucille’s case, for more measurable probabilities (or more beds), it does not. E.g. if there is a 20% chance of a man under one bed, then the chance of a man under either bed is 1-(0.8*0.8) or 36%.
This is extremely important when it comes to what is sold as “safe sex”. If your birth control / protection is 99.9% effective, but you use it 52 times in a year, it has to be effective all 52 times to be effective over all (ignoring cycles, which complicate the example but do not change the principle). The probability of all 52 times being effective is .999⁵² or 95%. After two years, the overall effectiveness is 90%.
An unexpected baby can be a blessing, but this much ignored mathematical fact is much more troublesome when it comes to alleged protection from diseases transmitted by promiscuity.