Probability of obtaining even number

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SUMMARY

The discussion revolves around calculating probabilities in two scenarios: rolling two six-sided dice and determining the probability of obtaining an even sum less than 8, and calculating the probability of selecting the first three horses in a race in the correct order. The first scenario concludes that the probability of rolling an even sum less than 8 is 4/36, or 1/9. The second scenario involves using conditional probability to find the likelihood of a specific horse finishing first, second, and third, resulting in a formula that incorporates the probabilities of each event occurring sequentially.

PREREQUISITES
  • Understanding of basic probability concepts, including events and outcomes.
  • Familiarity with conditional probability and the multiplication rule.
  • Knowledge of combinatorial counting principles, particularly permutations.
  • Ability to calculate probabilities for independent and dependent events.
NEXT STEPS
  • Study the concept of conditional probability in depth, focusing on the multiplication rule.
  • Learn about permutations and combinations to enhance understanding of betting scenarios.
  • Explore the probability distributions associated with rolling dice, specifically focusing on sums.
  • Practice solving probability problems involving multiple events to solidify understanding.
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Students studying probability theory, gamblers interested in betting strategies, and anyone looking to improve their understanding of statistical outcomes in games of chance.

有問題的人
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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.
 
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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.
 


cristo said:
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...
 


NVM~~ I got the first one


I just need to know how to do the second one
 


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!
 


HallsofIvy said:
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
 


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?
 


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?
 


nicksauce said:
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=
 
  • #10


HallsofIvy said:
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
 
  • #11


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.
 

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