MathDB

Daredevil Darren challenges Forgetful Fred to spell "Johns Hopkins." Forgetful Fred will spell it correctly except for the 's's; there is a

\frac{1}{3}

and

\frac{1}{4}

chance that he will omit the 's' in the first and last names, respectively, with his mistakes being independent of each other. If Forgetful Fred spells the name correctly, then he is happy; otherwise, Daredevil Darren will present him with a dare, and there is a

\frac{9}{10}

chance that Forgetful Fred will not be happy. Find the probability that Forgetful Fred will be happy.

Problem Statement