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On her way out of the toy store, Janelle stops to get $2$ gumballs from the giant gumball machine. Her favorite flavor is blue raspberry, but only about $30\%$ of the gumballs in the machine are blue. How likely is it that both of the gumballs Janelle gets will be blue? Janelle simulates the situation by putting $3$ blue marbles and $7$ yellow marbles in a bag. She picks a marble, then returns it to the bag, $2$ times. Each time a blue marble appears, it represents a blue gumball. Janelle records the results by writing ＂B＂ for a blue marble and ＂Y＂ for a yellow marble. Here are the results of $20$ trials: $\newline$YY, YB, YY, YY, BY, YB, YY, BB, BY, YY, YY, YB, YY, YY, BY, YY, BY, YY, BY, YY$\newline$ Based on Janelle's results, what is the probability that both of the gumballs will be blue?