# simple probability function

1. There are 4 identical squares laying horizontally like a ruler. Some connecting squares are selected at random and colored in blue to form a blue rectangle. Let X be the number of squares colored in blue. (A square is not considered as a rectangle in this case.)

a) find the probability function of X. Answer : x 2, 3, 4

P(X=x) 0.5, 1/3, 1/6

2. There are 9 small identical squares in the figure. At least 1 Small square is selected randomly and colored in red to form a red square. Let X be the number of small squares without color.

a) find the number of all possible outcomes. answer = 14

b) find the probability function of X. answer : x = 0,5,8 P(X=x) = 1/14, 2/7, 9/14

figure like this :

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1(a) X can only be 2,3 or 4

Shape no. of X

2 squares 3

3 squares 2

4 squares 1

Then P(2) = 3/6, P(3) = 2/6, P(4) = 1/6

2(a) To form a square, we should choose 1,4,9 small squares

So, the possible values of X are 8,5,0

X no. of X

8 9 (As you can take any one square to colour)

5 2 * 2 = 4

0 1 (Take all squares to colour)

No. of all possible outcomes = 14

(b) P(X = 0) = 1/14, P(X = 5) = 4/14, P(X = 8) = 9/14

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