Probability of obtaining even number

[有問題的人]

I have two probability questions..

and I have no clues staring them...

So... let's do this..

Two fair six-sided are rolled and the face values are added. What is the probability of obtaining a sum that is an even number less than 8?




There are 10 horses in a race. A particular bet requires a customer to choose the first three horses in the correct finishing order. If all 10 horses have an equal chance of finishing in any position, determine the probability that a single bet wins.

 

[cristo]

You need to show your work before we can help you. Please take a moment to read the homework help guidelines, as linked to in my signature.

 

[有問題的人]

You need to show your work before we can help you. Please take a moment to read the homework help guidelines, as linked to in my signature.

but I have no ideas about how to start this...

 

[有問題的人]

NVM~~ I got the first one


I just need to know how to do the second one

 

[HallsofIvy]

You just told us you had no idea how to even start the first one. Now, 3 minutes later you have finished it? Good, now try the second!

 

[有問題的人]

You just told us you had no idea how to even start the first one. Now, 3 minutes later you have finished it? Good, now try the second!

I can't conquer my brain... so... I need you guys' help

 

[nicksauce]

Ok maybe you need to review some basics. If A is an event with probability P(A) and B is an event with probability P(B), what is P(A and B)? After you've figured that out, can you state the second problem in a similar form?

 

[HallsofIvy]

There are 10 horses in the race and all are equally likely to win. What is the probability any specific one will win? What is the probability that the horse you bet on will win?

Given that, there are 9 horses left that might come in second and all are equally likely to come in second. What is the probability that the horse you bet on to place will place?

Given that, there are 8 horses left that might come in third and all are equally likely to come in third. what is the probability that the horse you bet on to show will show?

 

[有問題的人]

Ok maybe you need to review some basics. If A is an event with probability P(A) and B is an event with probability P(B), what is P(A and B)? After you've figured that out, can you state the second problem in a similar form?

Can't find the similarity =o=

 

[有問題的人]

There are 10 horses in the race and all are equally likely to win. What is the probability any specific one will win? What is the probability that the horse you bet on will win?

Given that, there are 9 horses left that might come in second and all are equally likely to come in second. What is the probability that the horse you bet on to place will place?

Given that, there are 8 horses left that might come in third and all are equally likely to come in third. what is the probability that the horse you bet on to show will show?

This is helpful~ thanks~ I got it

 

[nicksauce]

Now that you've got it, let me clarify to you what I wrote. We are looking for the probability that A wins the race, B gets second, and C gets third. (Assuming that you bet on A to win, B to get second and C to get third). We can write this as P(A gets first AND B gets second AND C gets third). Now we know (or we should know) that P(X AND Y) = P(X) * P(Y given X), thus the final probability becomes

P(A gets first AND B gets second AND C gets third) = P(A gets first)P(B gets second AND C gets third given that A gets first) = P(A gets first)P(B gets second given A gets first)P(C gets third given A gets first and B gets second)

This is in symbols what HallsOfIvy wrote in words.