Question

each unit square of a 3-by-3 unit-square grid is to be colored either blue or red. for each square, either color is equally likely to be used. what is the probability of obtaining a grid that does not have a 2-by-2 red square. (hint 14)

Answer 1

The probability of obtaining a grid that does not have a 2-by-2 red square 16 2/3%

probability : The probability of an event can be calculated by means of probability formula via honestly dividing the favorable quantity of outcomes by way of the total variety of viable consequences.

Step-by using-step clarification:

given that:

form are both square or circle with both equally likely :

for this reason,

P(square) = half of ; P(circle) = half of

color are either blue, pink or inexperienced with the 3 equally likely ;

P(purple) = 1/3 ; P(green) = 1/three ; P(blue) = 1/three

chance of creating a inexperienced circle :

independent probability

P(green n circle) = p(inexperienced) * p(circle)

P(green n circle) = 1/3 * half of

P(green n circle) = 1/6

= 0.16666

(0.16666 * 100%) = 16.6666%

= 16 2/3%

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