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help probability

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Two different numbers are selected simultaneously and at random from the set {1,2,3,4,5,6,7,8,9,10}. What is the probability that the positive difference between the two numbers is 3 or greater? Express your answer as a

common fraction.

Jul 2, 2022

#1
-1

The probability is 3/11.

Jul 3, 2022
#2
-1

There are:

[10 + 2 - 1] C 2 ==55 combinations as follows:

(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9) >>Total =  55 combinations

The probability is: 28 / 55

Jul 3, 2022
#3
+1

The above is with replacement. This is without replacement:

There are:

[10  C 2 ==45 combinations as follows:

( 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9) >>Total =  45 combinations

The probability is: 28 / 45

Guest Jul 3, 2022
#4
+1158
+1

nice job guest.

nerdiest  Jul 3, 2022