How do you use the Counting Principle to find the probability of choosing the 5 winning lottery numbers when the numbers are chosen at random from 0 to 9?

taumulurtulkyoy
2022-10-20
Answered

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Kash Osborn

Answered 2022-10-21
Author has **18** answers

We have a 5-digit number and we're trying to calculate the odds of guessing the number correctly.

For each digit, there is a 1/10 chance of getting it right. There are 5 digits, and so according to the Counting Principle, we multiply all of them together:

$\left(\frac{1}{10}\right)\left(\frac{1}{10}\right)\left(\frac{1}{10}\right)\left(\frac{1}{10}\right)\left(\frac{1}{10}\right)=\frac{1}{{10}^{5}}=\frac{1}{10,000}=0.0001$

For each digit, there is a 1/10 chance of getting it right. There are 5 digits, and so according to the Counting Principle, we multiply all of them together:

$\left(\frac{1}{10}\right)\left(\frac{1}{10}\right)\left(\frac{1}{10}\right)\left(\frac{1}{10}\right)\left(\frac{1}{10}\right)=\frac{1}{{10}^{5}}=\frac{1}{10,000}=0.0001$

asked 2022-06-15

Three friends agreed to meet at 8 P.M. in on of the Spanish restaurants in town. Unfortunately they forgot to specify the name of the restaurant. If there are 10 Spanish restaurants

(a) find the number of ways they could miss each other

(b) find the number of ways they could meet

(c) find the number of ways at least two of them meet each other.

I got 10 * 3 = 30 ways for (a) for (b), I got 10 ways. how do I do (c)?

(a) find the number of ways they could miss each other

(b) find the number of ways they could meet

(c) find the number of ways at least two of them meet each other.

I got 10 * 3 = 30 ways for (a) for (b), I got 10 ways. how do I do (c)?

asked 2022-09-27

There are $\frac{m}{gcd(m,x)}$ distinct elements in the set $\{ax\phantom{\rule{0.444em}{0ex}}(\mathrm{mod}\phantom{\rule{0.333em}{0ex}}m):a\in \{0,...,m-1\}\}$

I have only known these by using a computer to generate the number of distinct elements. But I am not sure how to prove this conjecture.

And is there any way that we can connect this problem to Euler's phi function so that we can simply use properties of $\varphi $ function to prove it?

And can we also use some counting principle here to give an exact answer?

I have only known these by using a computer to generate the number of distinct elements. But I am not sure how to prove this conjecture.

And is there any way that we can connect this problem to Euler's phi function so that we can simply use properties of $\varphi $ function to prove it?

And can we also use some counting principle here to give an exact answer?

asked 2022-07-02

50 students traveled to Europe, last year. Of these, 12 visited Amsterdam, 13 went to Berlin, and 15 were in Copenhagen. Some visited two cities: 3 visited both Amsterdam and Berlin, 6 visited Amsterdam and Copenhagen, and 5 visited Berlin and Copenhagen. But only 2 visited all three cities.

Question : How many students visited Copenhagen, but neither Amsterdam nor Berlin?

I have done the graph and I think the answer is 6 but I would like to learn how to compute it.

Question : How many students visited Copenhagen, but neither Amsterdam nor Berlin?

I have done the graph and I think the answer is 6 but I would like to learn how to compute it.

asked 2022-05-08

1. Sailing ships used to send messages with signal flags flown from their masts. How many different signals are possible with a set of four distinct flags if a minimum of two flags is used for each signals?

2. A Gr. 9 students may build a timetable by selecting one course for each period, with no duplication of courses. Period 1 must be science, geography, or physical education. Period 2 must be art, music, French, os business. Period 3 and 4 must be math or English. How many different timetables could a student choose?

2. A Gr. 9 students may build a timetable by selecting one course for each period, with no duplication of courses. Period 1 must be science, geography, or physical education. Period 2 must be art, music, French, os business. Period 3 and 4 must be math or English. How many different timetables could a student choose?

asked 2022-07-09

I've been studying stats, and currently taking my first ever engineering based stats course in college. It covers Probability extensively and other stats topics. Currently, I'm stuck on recognizing key points in a problem involving permutations / combinations vs. fundamental counting principle. I have 2 example problems and what would help the most is key things to look to recognize using the counting principle vs permutations / combinations formulas. Here's one that uses the permutations / combinations according to my student solutions manual

A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet (he only drinks red wine), all from different wineries.

If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this?

If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this?

If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety?

If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen?

If 6 bottles are randomly selected, what is the probability that all of them are the same variety?

Here's one that uses counting principle

The composer Beethoven wrote 9 symphonies, 5 piano concertos (music for piano and orchestra), and 32 piano sonatas (music for solo piano).

a) How many ways are there to play first a Beethoven symphony and then a Beethoven piano concerto?

b) The manager of a radio station decides that on each successive evening (7 days per week), a Beethoven symphony will be played followed by a Beethoven piano concerto followed by a Beethoven piano sonata. For how many years could this policy be continued before exactly the same program would have to be repeated?

Any ideas would be helpful to recognize the clues in the problems.

A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet (he only drinks red wine), all from different wineries.

If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this?

If 6 bottles of wine are to be randomly selected from the 30 for serving, how many ways are there to do this?

If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety?

If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen?

If 6 bottles are randomly selected, what is the probability that all of them are the same variety?

Here's one that uses counting principle

The composer Beethoven wrote 9 symphonies, 5 piano concertos (music for piano and orchestra), and 32 piano sonatas (music for solo piano).

a) How many ways are there to play first a Beethoven symphony and then a Beethoven piano concerto?

b) The manager of a radio station decides that on each successive evening (7 days per week), a Beethoven symphony will be played followed by a Beethoven piano concerto followed by a Beethoven piano sonata. For how many years could this policy be continued before exactly the same program would have to be repeated?

Any ideas would be helpful to recognize the clues in the problems.

asked 2022-04-30

I'm missing something here. Let $X=\{(123),(132),(124),(142),(134),(143),(234),(243)\}$, ${A}_{4}$ act on $X$ by conjugation (inner automorphisms) and $x=(123)$, then $4=|\mathcal{O}(x)|=|G|/|{G}_{x}|=12/|{G}_{x}|$. However, ${G}_{x}=\{1\}$

What's wrong here?

What's wrong here?

asked 2022-06-20

I believe this question involves the rule of sum and the fundamental counting principle. I think my logic here is wrong, but I hope you could correct it.

(26 P 2 + 26 P 3)(10 P 4) = 8.19*10^7

(26 P 2 + 26 P 3)(10 P 4) = 8.19*10^7