Let B = No of black marbles in the jar

If B = 1, Pr(observations) = (99/100)^100 = 0.366

If B = 2, Pr(observations) = (98/100)^100 = 0.133.   etc. etc.

Summing all these probabilities from B = 1 to B = 99 gives 0.572 which is probability of observing no black marbles in 100 draws given any number of black marbles actually present in the jar.

Hence probability that jar has only white marbles is 1 – 0.572 = 0.428