Digit d is randomly selected from the set {1, 2, 3, 4, 5, 6, 7, 8,
9}. Without replacement of d, another digit, e is selected. What
is the probability that the two digit number de is a multiple of 3?
This is not a calculus question. Please label the subject correctly
To find the probability that the two-digit number "de" is a multiple of 3, we need to determine the combinations of digits (d and e) that satisfy this condition and divide it by the total number of possible combinations.
Step 1: Determine the total number of possible combinations
Since we are randomly selecting two digits from the set {1, 2, 3, 4, 5, 6, 7, 8, 9}, there are a total of 9 options for the first digit (d) and 8 options for the second digit (e), giving us a total of 9 * 8 = 72 possible combinations.
Step 2: Determine the combinations that result in a multiple of 3
To have a two-digit number that is a multiple of 3, the sum of the digits (d + e) must be divisible by 3. We can list the possible combinations that satisfy this condition:
(1, 2), (1, 5), (1, 8), (2, 1), (2, 4), (2, 7), (3, 3), (3, 6), (3, 9), (4, 2), (4, 5), (4, 8), (5, 1), (5, 4), (5, 7), (6, 3), (6, 6), (6, 9), (7, 2), (7, 5), (7, 8), (8, 1), (8, 4), (8, 7), (9, 3), (9, 6), (9, 9)
Counting the combinations, we find that there are 27 combinations that result in a multiple of 3.
Step 3: Calculate the probability
To find the probability, divide the number of combinations resulting in a multiple of 3 (27) by the total number of possible combinations (72):
Probability = (Number of favorable outcomes)/(Total number of possible outcomes)
= 27/72
= 3/8
= 0.375
Therefore, the probability that the two-digit number "de" is a multiple of 3 is 0.375 or 37.5%.