The probability of getting fewer than 20 heads in 54 flips of a fair coin can be calculated using the binomial distribution. The binomial distribution gives the probability of getting exactly k successes (defined as getting a head in this case) in n trials (flips), when the probability of success on any given trial is p.

The formula for the binomial distribution is:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))

where:
- P(X=k) is the probability of getting k successes in n trials,
- C(n, k) is the number of combinations of n items taken k at a time,
- p is the probability of success on any given trial (0.5 for a fair coin),
- n is the number of trials (54 in this case),
- k is the number of successes (we want fewer than 20, so we'll have to sum up the probabilities for k=0 to 19).

So, the probability of getting fewer than 20 heads in 54 flips is:

P(X<20) = Σ P(X=k) for k=0 to 19
= Σ [C(54, k) * (0.5^k) * ((1-0.5)^(54-k))] for k=0 to 19

This calculation involves a lot of computation, so it's best done with a computer or a calculator with statistical functions.

Using a binomial calculator, we find that the probability of getting fewer than 20 heads in 54 flips of a fair coin is approximately 0.0405 or 4.05%.

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