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Problem 1. Each of Ivan and Peter choose a random natural number from 1 to 10. What is the probability that the number of Peter is larger than the number of Ivan?

P = 45/100 = 0,45

You can figure it out from the graphics of problem 1 on the page:

http://www.cphpvb.net/probability/6565-larger-random-number/

Problem 1'. Each of Ivan and Peter choose a random natural number from 1 to 10. What is the probability that the number of Peter is larger OR EQUAL than the number of Ivan?

P = 55/100 = 0,55

Problem 1''. Each of Ivan and Peter choose a random natural number from 1 to 100. What is the probability that the number of Peter is larger than the number of Ivan and what is the probability that the number of Peter is larger or equal than the number of Ivan?

P(a) = 4950/10000 = 0,495

P(b) = (4950+100)/10000 = 0,505

Problem 2. Each of Ivan and Peter choose a random natural number from 1 to 10. What is the probability that the number of Peter is larger than the number of Ivan and at the same time the number of Peter is lower than 5?

P(y>x | y<5) = 6/100 = 0,06

first graphic from:

http://www.cphpvb.net/probability/6571-two-conditions/

Problem 3. Each of Ivan and Peter choose a random natural number from 1 to 10. What is the probability that the number of Peter is larger than the number of Ivan and at the same time the number of Ivan is lower than 5?

P(y>x | x<5) = 30/100 = 0,30

the second graphic from:

http://www.cphpvb.net/probability/6571-two-conditions/

Problems for you:

1. Find P(y>x | x<5 | y<5) where y is Peter and x is Ivan

2. Find P(x>y | y>2 | x<8)

3. Find the solutions of the problems with REAL numbers instead of natural

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Problems for you:

1. Find P(y>x | x<5 | y<5) where y is Peter and x is Ivan

2. Find P(x>y | y>2 | x<8)

3. Find the solutions of the problems with REAL numbers instead of natural

1. x,y in {1, 2, 3, 4}=> P = 6/16 = 3/8

2. assumption: y < 8 => x in {1, 2, 3, 4, 5, 6, 7}, y in {3, 4, 5, 6, 7} => P = 10/35 = 2/7

3. problem can be solved by drawing the lines on a graph and calculating the area. All .gt. shall be replaced with .gte. and .lt. with .lte.

Thus P1=0.5 and P2=0.375

Edited by KlueMaster
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