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# Help with these 2 problems

Hey guys! Hope you can help me.

1-We consider a square of lenght 6 cm. From the middle of every side you draw 2 segments that join the middle of the side with the vertexs of the opposite side. Hence we get an octogon. What is the area of this octogon?

I get $$\frac{9\sqrt{2}}{2}$$

Am I right?

2-A dice has 2 faces with number 1 and 4 faces with number 2. We toss it 6 consecutive times. What is the probablity that at least in 2 consecutive throws we get the same number? .

Note by Juan Rodrígez
3 years, 9 months ago

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For #2 you could approach it with P (X) = 1 - P (not X) as there are a lot of possibilities in consideration

P (not X) = all alternating P (not X) = P (1,2,1,2,1,2) or P (2,1,2,1,2,1) because they are mutually exclusive you could just add them

P (not X) = P ( 1,2,1,2,1,2) + P (2,1,2,1,2,1)

P (not X) = 1/3 * 2/3 * 1/3 * 2/3 * 1/3 * 2/3 + 2/3 * 1/3 * 2/3 * 1/3 * 2/3 * 1/3

P (not X) = (1/3)^{3} * (2/3)^{3} + (2/3)^{3} * (1/3)^{3}

P (not X) = 2 * [ (1/3)^{3} * (2/3)^{3} ]

P (not X) = 2^{4} / 3^{6}

P (X) = 1 - 2^4 / 3^6

p.s. edited because I need to study the formatting guide xD · 3 years, 9 months ago

for the first one u r rite.. :) · 3 years, 9 months ago