Discrete Math - quick probability questions.

In summary, the multiplication rule can be used with a twist to find integers that contain the digit 6 at least once.
  • #1
KingsFoil
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For the life of me I am having a hard time understanding how to do problems of this nature. As I understand it, were using the multiplication rule here with a twist.a. How many integers from 1 through 100,000 contain the
digit 6 exactly once?

5 * 9 * 9 * 9 * 9 = 38805 is what I have. Because the digit 6 can appear in 5 different locations.

b. How many integers from 1 through 100,000 contain the
digit 6 at least once?

c. If an integer is chosen at random from 1 through
100,000, what is the probability that it contains two or
more occurrences of the digit 6?

I am clueless here. Add up all the possibilities of containing two 6's...three 6's... four 6's... five 6's and then divide by the total possibilities.That's my line of thinking... I am just not sure how to find the amount of possibilities for each partition.
 
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  • #2
KingsFoil said:
b. How many integers from 1 through 100,000 contain the
digit 6 at least once?

How many integers are there that do not contain any digit 6?
 
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  • #3
KingsFoil said:
b. How many integers from 1 through 100,000 contain the
digit 6 at least once?

The first thing I always try in probability problems is to invert it. P(X) = 1 - P(not X)
It's easy to give it a shot, and often the resulting problem is much simpler.

In this case not X is
b') How many integers from 1 through 100,000 do not contain digit 6?
I bet that you can do that.

KingsFoil said:
c. If an integer is chosen at random from 1 through
100,000, what is the probability that it contains two or
more occurrences of the digit 6?

I am clueless here. Add up all the possibilities of containing two 6's...three 6's... four 6's... five 6's and then divide by the total possibilities.That's my line of thinking... I am just not sure how to find the amount of possibilities for each partition.

Try my special magic rule again.
 
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Related to Discrete Math - quick probability questions.

1. What is the definition of probability in discrete math?

In discrete math, probability refers to the measure of the likelihood of an event occurring, given a set of possible outcomes. It is typically represented as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

2. What is the difference between independent and dependent events in discrete math?

Independent events are those where the occurrence of one event does not affect the probability of another event occurring. On the other hand, dependent events are those where the occurrence of one event affects the probability of another event occurring.

3. How do you calculate the probability of an event in discrete math?

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical probability formula: P(E) = Number of favorable outcomes / Total number of possible outcomes.

4. What is the difference between theoretical and experimental probability in discrete math?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. On the other hand, experimental probability is based on actual observations and can vary from the theoretical probability due to chance or other factors.

5. How does the concept of permutations and combinations relate to probability in discrete math?

Permutations and combinations are used to determine the number of possible outcomes in a given situation, which is essential in calculating probabilities. Permutations refer to the arrangement of a set of objects, while combinations refer to the selection of a subset from a larger set.

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