Once upon a time, a princess was walking through a forest and stumbled across a pond. Out of the pond rose a witch, who cackled, \"Stop! I have turned a handsome prince into a frog and cast him into my pond to live with 99 other frogs. Each frog has a different number on his back. The prince has the largest number on his back, and this is your only way of spotting him. You must find him and kiss him if you want to leave my enchanted forest. The frogs will jump from the pond one by one. When each frog appears, you must decide whether to kiss him or throw him back in, never to be seen again. If you kiss a real frog, or don't kiss any of the 100 frogs, you will never leave the forest, and the prince will remain in the pond.\" And with a suitably evil laugh, the witch sank back into her murky pond. Fortunately, the princess was very good at maths, and knew the best strategy for deciding which frog to kiss.

She repeated this for the first 37 frogs, and noted that the highest number she had seen so far was 23.2. She then waited until she saw a frog numbered higher than 23.2 and kissed it. (Of course the frog numbered 23.2 might have been the prince, and she'd then have missed him.)

How much is the risk that the she kisses wrong frog?

Is the risk less than she wait for the first 20, 30, 50 or 60 frogs?

Please Use Excel