Difficulty: pretty easy. Kids will get wrapped up in the P(A) and if-then, but it's an example of a problem that is much easier if you imagine the grid of all possibilities. Definitely a candidate for the SAT.
Problem 27
Difficulty: Medium. It's funny how easily the kids get thrown by an infinite series.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 15 and answer 27.
I like the triangle. Consider the whole figure. Base is 1. Height of the complete triangle will be , hmm, base 1/4, ht 1/2, completed base 1/2 (twice), height 1.
ReplyDeleteSO the area of the triangle is 1/2. And on each row, one third is triangle, 2/3 are square, so 1/3 of 1/2 is...
Now, for the dice, there are many interesting complications, but for many, probability, even without complications, is hard.