Step-by-step explanation: GIVEN: Two digit number means we will have to choose from numbers 0-9 for the second digit and 1-9 for the first digit. (since zero can't be in the tens place) Formula: We will use m x n. That is, m is the number of elements we can use for the first digit and n will be the number of elements we can use for the second digit. Sample Space: To get the probability, we must find the sample space or all the outcomes. m - 9 elements (1-9) m - 9 elements (1-9)n - 10 elements (0-9) m x n = 9x10 =90 90 is our sample space. A. An odd number Conditions: For an odd number, the second number will determine whether or not it is an odd number. For the first digit, we can use 1-9. Elements: m - 9 elements (1-9) m - 9 elements (1-9)n - 5 elements (1,3,5,7,9) m x n=9x5=45 SOLVE (probability) Probability= possible outcomes/sample space P=45/90 P=1/2 B. Larger than 75. Conditions: The first digit could be equal to 7 or greater. But n will only be greater than 5 if and only if m=7 and n could be any number if m>7. Elements 1: m - 1 element (7) m - 1 element (7)n - 4 elements (6,7,8,9) m - 1 element (7)n - 4 elements (6,7,8,9)m x n=1x4=4 Elements 2: m - 2 elements (8,9) m - 2 elements (8,9)n - 10 elements (0,1,2,3,4,5,6,7,8,9,) m - 2 elements (8,9)n - 10 elements (0,1,2,3,4,5,6,7,8,9,)mxn=2x10=20 TOTAL: 4+20=24 SOLVE (PROBABILITY) Probability= possible outcomes/sample space P=24/90 P=4/15 C. multiple of 5 Condition: the second digit must be either 0 or 5 and the first digit could be any digit. Elements: m - 9 elements (1-9) m - 9 elements (1-9)n - 2 elements (0,5) m x n =9x2=18 SOLVE (PROBABILITY) P=18/90 P=1/5 D. An even number smaller than 40 Condition: The first digit could be equal to 4 but the second digit must be even (excluding zero). Another situation is the first digit would be greater than 4 and the second digit would be any even number. Elements 1: m - 1 element (4) n - 4 elements (2,4,6,8) m x n = 1x4=4 Elements 2: m - 5 elements (5,6,7,8,9) n - 5 elements (0,2,4,6,8) mxn=5x5=25 TOTAL: 25+4=29 SOLVE: Probability P=29/90
