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mathelord
What Is The Probability Of Picking A 3 Digit Number Divisible By 7
The probability of picking a 3 digit number divisible by 7 is 1/7 or approximately 14.29%. This is because there are 10 possible numbers for each place value (0-9), and only one of those numbers (7) is divisible by 7. So the probability is 1 out of 10 for the hundreds place, 1 out of 10 for the tens place, and 1 out of 10 for the ones place, giving a total probability of 1/10 * 1/10 * 1/10 = 1/1000. However, since we are only considering 3 digit numbers, we need to multiply this by the number of possible combinations, which is 9 * 10 * 10 = 900. This gives a final probability of 1/1000 * 900 = 9/1000 = 1/7.
The probability of picking a 3 digit number divisible by 7 can be calculated by dividing the number of favorable outcomes (3 digit numbers divisible by 7) by the total number of possible outcomes. In this case, the total number of possible outcomes is 900 (9 * 10 * 10) and the number of favorable outcomes is 128 (9 * 1 * 10 + 9 * 2 * 10 + 9 * 3 * 10 = 900). So the probability is 128/900, which can be simplified to 8/45.
The theoretical probability of picking a 3 digit number divisible by 7 is 1/7 or approximately 14.29%, as explained in the first question. The experimental probability, on the other hand, can be determined by actually conducting a experiment and recording the results. For example, if we randomly select 100 3 digit numbers, we may find that only 10 of them are divisible by 7, giving an experimental probability of 10/100 = 10%.
One way to increase the probability of picking a 3 digit number divisible by 7 is to increase the sample size. This means picking more 3 digit numbers, which will give a more accurate representation of the theoretical probability. Another way is to limit the range of numbers that can be selected. For example, if we only allow 3 digit numbers from 100 to 200, the probability of picking a number divisible by 7 is much higher (10/100 = 10%).
Other factors that might affect the probability of picking a 3 digit number divisible by 7 include the number of digits allowed (3, 4, 5, etc.), the range of numbers allowed, and whether or not repetition of digits is allowed. For example, if we allow 4 digit numbers and repetition of digits, the probability of picking a number divisible by 7 will increase. Additionally, if we limit the range of numbers to only those with a certain pattern (e.g. all digits are the same), the probability may also increase.