Counting and probablity addition rule?

In summary, a calculator with an eight-digit display can display up to 10,000,000 distinct numbers, taking into account the decimal point and minus sign. However, if we consider numbers with trailing zeros to be equal, the number of distinct numbers would be significantly less and would require dealing with each "length" separately to avoid double-counting.
  • #1
Tleeves
1
0
A calculator has an eight -digit display and a decimal point that is located at the extreme right of the number displayed, at the extreme left or between any pair of digits. The calculator can also display a minus sign at the etreme left of the number. How many distinct numbers can the calculator display? (not the certain numbers are equal, such as 1.9, 1.90, 01.900, and should, therefore, not be counted twice.)

i have
12 choices for the first digit , 10 for the 2nd, 9 for the 3rd, 8 for the 4th, 7 for the 5th, 6 for the 6th, 5 for the 7th, 4 for the 8th.

But this is using the multiplication rule and doesn't account for the numbers such as 1.9, 1.90, 01.900 which the addition rule would. I can't figure out else to do it and am not sure if I'm supposed to use the addition rule.
 
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  • #2
Welcome to PF!

Hi Tleeves! Welcome to PF! :smile:
Tleeves said:
… 12 choices for the first digit , 10 for the 2nd, 9 for the 3rd, 8 for the 4th, 7 for the 5th, 6 for the 6th, 5 for the 7th, 4 for the 8th.

uhh? except for the repetitions, it would be 10 choices for the first digit , 10 for the 2nd, 10 for the 3rd, … 10 for the 8th.

I think you'll need to deal with each "length" separately (where the length of a number would be the length from the first non-zero digit to the last non-zero digit), to avoid double-counting the repetitions.
 

Related to Counting and probablity addition rule?

1. What is counting and probability addition rule?

The counting and probability addition rule is a principle in probability theory that states that the probability of two or more events occurring is equal to the sum of their individual probabilities. It is used to calculate the likelihood of a combination of events happening together.

2. How is the counting and probability addition rule applied?

The counting and probability addition rule is applied by first determining the individual probabilities of each event and then adding them together. This can be done by using the formula P(A or B) = P(A) + P(B) - P(A and B), where P(A) and P(B) are the individual probabilities and P(A and B) is the probability of both events occurring together.

3. What is the difference between dependent and independent events in the counting and probability addition rule?

In the counting and probability addition rule, dependent events are those that affect each other's probability, while independent events are those that do not. For example, if you flip a coin and then roll a die, these events are independent because the outcome of one does not affect the outcome of the other. However, if you draw two cards from a deck without replacing the first one, these events are dependent because the probability of drawing the second card is affected by the outcome of the first draw.

4. Can the counting and probability addition rule be used for more than two events?

Yes, the counting and probability addition rule can be used for any number of events. The formula for calculating the probability of multiple events occurring is P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C). This formula can be extended to any number of events.

5. How is the counting and probability addition rule related to the concept of sample space?

The counting and probability addition rule is related to the concept of sample space because in order to calculate the probability of multiple events, we must first determine the total number of possible outcomes in the sample space. This is known as the denominator in probability calculations. The counting and probability addition rule then allows us to determine the probability of specific combinations of events occurring within the sample space.

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