How Do Basic Permutations Apply to Real-World Probability Problems?

[F.B]

I have some more questions but this time, you can use permutations but basic basic ones because i was reading ahead in my book, because my teacher won't explain it anyway.

Heres the question from the last thread of mine but there's something i didn't post.

1. A basketball player has a success rate of 80% for shooting free throws.
Calculate the following probabilities.

iv) She will make at least three out of five attempts.

I know how to do the other parts that you guys helped me with but this one is different.

2. Postal codes for Canada have the form LDL DLD, where L is any letter from A to Z, and D is any digit from 0 to 9. Some letters may not be permitted in certain positions of the postal code by Canada Post. As a result, the actual number of allowable postal codes will be different from the total number possible.
a)Estimate the total number of possible postal codes available for use in Canada.
b)Postal codes for Toronto start with the letter M. What is the probability that a postal code selected randomly an area in Toronto.


3. A health and safety committee is to be selected from all people who work at a local factory. The committee is to consist of four members randomly selected from a list of ten names submitted by the shop leader. The list has the names of 5 union members and 5 works who are not union members.

a)What is the probability that the first two people selected from the list are union members?
b)what is the probability that all the committee members are union members?

By the way all these question are in the section before we learn about permutations. But if you can't avoid it then use permutations because i want to learn how to do them also. But use basic ones.

 

[F.B]

I know there's are a lot of questions but please help me

 

[HallsofIvy]

I have some more questions but this time, you can use permutations but basic basic ones because i was reading ahead in my book, because my teacher won't explain it anyway.
Heres the question from the last thread of mine but there's something i didn't post.
1. A basketball player has a success rate of 80% for shooting free throws.
Calculate the following probabilities.
iv) She will make at least three out of five attempts.

"At least" 3 out of 5. You already saw how to do exactly 3 out of 5. At least 3 out of 5 includes exactly 4 and exactly 5. You should be able to work those out from what you were shown before. Probability of a success is 0.80 so probability of failure is 0.20. Probability of making 4 in a row and missing the last, SSSSF, is (.8)(.8)(.8)(.8)(.2). But what about SSSFS, SSFSS, SFSSS, and FSSSS? It should be easy to calculate the probability of hitting all 5 shots. Now add all of those together.

I know how to do the other parts that you guys helped me with but this one is different.
2. Postal codes for Canada have the form LDL DLD, where L is any letter from A to Z, and D is any digit from 0 to 9. Some letters may not be permitted in certain positions of the postal code by Canada Post. As a result, the actual number of allowable postal codes will be different from the total number possible.
a)Estimate the total number of possible postal codes available for use in Canada.

26 choices for L, 10 for D. So LDL DLD is (26)(10)(26)(10)(26)(10).

b)Postal codes for Toronto start with the letter M. What is the probability that a postal code selected randomly an area in Toronto.

Since you are required to start with M, all Toronto codes are of the form MDL DLD. There is only one M but again 10 possiblities for each D and 26 for each L. How many possible codes are there like that? What fraction of all possible codes (from a) is that?

3. A health and safety committee is to be selected from all people who work at a local factory. The committee is to consist of four members randomly selected from a list of ten names submitted by the shop leader. The list has the names of 5 union members and 5 works who are not union members.
a)What is the probability that the first two people selected from the list are union members?

5 out of 10 names are union members. What is the probability that the first person selected is a union member? If the first person selected is a union member, that leaves 9 people, 4 of whom are union members. What is the probability that the second person selected is a union member? Now multiply those together.

b)what is the probability that all the committee members are union members?

Just continue (a) to the third and fourth members.

By the way all these question are in the section before we learn about permutations. But if you can't avoid it then use permutations because i want to learn how to do them also. But use basic ones.

1)iv) is easier using permutation formulas but it's not necessary. I didn't use permutations in the other problems.