Math Problems, Probability Problems

Problem of the Day: 12/17/12

If three coins are flipped at the same time, what is the probability that none will land on tails? Express your answer as a common fraction.

(A common fraction is a fraction in the form a/b where a and b are integers with no common factors besides 1 – a.k.a. a fraction in simplest form.)

Explanation of yesterday’s problem:
Here’s the diagram again:

20121217-065132.jpg
In the picture, angles A and B are congruent. Therefore triangle ABC is isosceles. Then we know that sides AB and BE are congruent also. If the base and one of the legs are congruent, then we know both legs are congruent to the base – the triangle is equilateral. All angles in an equilateral triangle are 60°. So angle AEB is also 60°.
By vertical angles, angle CED is 60°. As in any triangle, the angles add up to 180°, so the sum of angles X and Y is 180° minus angle CED, or 180 – 60 = 120°.

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