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? .

#Geometry #HelpMe! #MathProblem #Math

Easy Math Editor

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Comments

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

Christian Barrera - 7 years, 7 months ago

Question 1 had an answer of 14cm^2.the octagon is 7/9 the half of the square's area.

Sharky Kesa - 7 years, 7 months ago

for the first one u r rite.. :)

Ramesh Goenka - 7 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$