The most complicated probability is the one that you asked - the probability that a 7 doesn't occur before any other number. It involves 1023 terms. Fortunately, it is the last term that the program computes, so all I had to do to get your answer was to have the program output this final probability. The probability of rolling a 7 would be 6/36 = 1/6 = 0.167 = 16.7%! Another way of thinking about the craps game is thinking that since there is a 1 in 6 chance that a 7 will be rolled, there is a 5 in 6 chance that a 7 will not be rolled. So betting on a point number in this case or betting for the shooter to not roll a 7 is a great bet as 5. Tree diagrams, conditional probablitity, compound events. (Sections 5 – 7) Discussion and mathematical analysis of the dice game Craps. (Supplemental Notes) Introduction to basic combinatorics (Sections 8- 10) Using basic combinatorics to help analyze the probabilities associated with poker (Supplemental Notes).
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I'm a CJ/CIS major working in a Math department, and I've been asked to convert an open ended question test to multiple choice test. I found your site 'The Wizard of Odds', and was directed here to ask my question. What is the probability of rolling a 2 given your roll only being even, when rolling a 20 sided die? Thank you for your help.
-R
Hey Wizard,
I'm a CJ/CIS major working in a Math department, and I've been asked to convert an open ended question test to multiple choice test. I found your site 'The Wizard of Odds', and was directed here to ask my question. What is the probability of rolling a 2 given your roll only being even, when rolling a 20 sided die? Thank you for your help.
-R
I know what you probably meant, but you actually need to specify what's on the 20-sided die. If it's 10 through 200 in increments of 10, the probability is zero.
Under the assumption that the d20 contains integers 1.20, here are the answers I'd list on a four-choice pick:
a) 1/2
b) 1/5
c) 1/10
d) 1/20
Edit: What's a 'CJ' major?
Administrator
Craps Conditional Probability Calculator
I know what you probably meant, but you actually need to specify what's on the 20-sided die. If it's 10 through 200 in increments of 10, the probability is zero.
Under the assumption that the d20 contains integers 1.20, here are the answers I'd list on a four-choice pick:
a) 1/2
b) 1/5
c) 1/10
d) 1/20
Edit: What's a 'CJ' major?
Funny, I read it differently for the same reason. I 'decided' the question stipulated the 20 sides were numbered 2 thru 20, evens only, with 2 identical sides per number, before I read ME's answer. Be interested to see the clarification.
I'm guessing 'Criminal Justice/Crime Scene Investigation' for the major.
I played some Dungeons & Dragons as a kid, so I've seen a d20 or two.
With a d20 (integers 1 through 20) the odds of rolling a 2 would be (drum roll please).. 1 in 20.
If you're saying 'I've got a d20. The next roll will be an even number. What are the odds of that number being a 2?' Then I'd have to say the odds are 1 in 10. But how does one guarantee that no odd number will be rolled?
I'm thinking CJ/CIS is Criminal Justice/Criminal Information Systems.
If you're saying 'I've got a d20. The next roll will be an even number. What are the odds of that number being a 2?' Then I'd have to say the odds are 1 in 10. But how does one guarantee that no odd number will be rolled?
It's a conditional probability problem. It's guaranteed because the question says it's guaranteed. It's a math question, not a physics question.
My HS world geography teacher was a sadistic guy. He put patterns into all his tests, but he also rotated the correct answers. So my 100% score could go a,b,c,d,a,b,c,d.. while my friend could have the same answers but need to respond d,c,b,a,d,c,b,a.. Made colluding and/or selling answers a real pain.
Craps Probabilities
Craps Conditional Probability Rules
I'm sorry, fellas. The numbers on the dice are 1-20. My understanding of this questions is, what is the probability you will roll an even number and what is the probability that even number will be 2? The next question on the test is 'Find the probability of drawing a king given that you draw a spade.' I'm pretty sure both questions require the same method to solve.
CJ - Criminal Justice
The numbers on the 20 sided dice are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. If this reply sounds smartalically, I appologize. I don't really understand what you mean needing to 'specify what's on the 20-sided die.' Anyhow, which is the answer; a, b, c, or d?
There are 10 even numbers. If you know for sure that it is even, then the answer is 1/10.
You can also solve this by going through the formula for conditional probability. To be honest I always have to look it up (check wikipedia for conditional probability), but you will end up dividing 1/20 by 10/20 and get 1/10.
'But how does one guarantee that no odd number will be rolled?' Probable probability.
Thank you.
1.4-13 Tn the gambling game 'craps' a pair of dice is rolled and the outcome of the experiment is the sum of the points on the up-sides of the six-sided dice. The bettor wins on the first roll if the sum is 7 or 11. The bettor loses on the first roll if the sum is 2, 3, or 12. If the sum is 4, 5, 6, 8, 9, or 10, that number is called the bettor's 'point.' Once the point is established, the rule is, If the bettor rolls a 7 before the 'point,' the bettor loses; hut if the 'point' is rolled before a 7, the bettor wins.
(a) List the 36 outcomes in the sample space for the roll of a pair of dice. Assume that each of them has a probability of 1/36.
(b) Find the probability that the bettor wins on the first roll. That is, fInd the probability of rolling a 7 or ii, P(7 or 11).
(c) Given that 8 is the outcome on the first roll, find the probability that the bettor now rolls the point 8 before rolling a 7 and thus wins. Note that at this stage in the game the only outcomes of interest are 7 and 8. Thus find P(8 | 7 or 8).
(d) The probability that a bettor rolls an 8 on the first roll and then wins is given by P(8)P(8 | 7 or 8). Show that this probability is (5/36)(5/11).
(e) Show that the total probability that a bettor wins in the game of craps is 0.49293.
HINT: Note that the bettor can win in one of several mutually exclusive ways: by rolling a 7 or ii on the first roll or by establishing one of the points 4, 5, 6. 8, 9, or 10 on the first roll and then obtaining that point before a 7 on successive rolls.
https://brainmass.com/math/probability/conditional-probability-gambling-146405
Attachments
Hey Wizard,
I'm a CJ/CIS major working in a Math department, and I've been asked to convert an open ended question test to multiple choice test. I found your site 'The Wizard of Odds', and was directed here to ask my question. What is the probability of rolling a 2 given your roll only being even, when rolling a 20 sided die? Thank you for your help.
-R
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I know what you probably meant, but you actually need to specify what's on the 20-sided die. If it's 10 through 200 in increments of 10, the probability is zero.
Under the assumption that the d20 contains integers 1.20, here are the answers I'd list on a four-choice pick:
a) 1/2
b) 1/5
c) 1/10
d) 1/20
Edit: What's a 'CJ' major?
Administrator
Craps Conditional Probability Calculator
I know what you probably meant, but you actually need to specify what's on the 20-sided die. If it's 10 through 200 in increments of 10, the probability is zero.
Under the assumption that the d20 contains integers 1.20, here are the answers I'd list on a four-choice pick:
a) 1/2
b) 1/5
c) 1/10
d) 1/20
Edit: What's a 'CJ' major?
Funny, I read it differently for the same reason. I 'decided' the question stipulated the 20 sides were numbered 2 thru 20, evens only, with 2 identical sides per number, before I read ME's answer. Be interested to see the clarification.
I'm guessing 'Criminal Justice/Crime Scene Investigation' for the major.
I played some Dungeons & Dragons as a kid, so I've seen a d20 or two.
With a d20 (integers 1 through 20) the odds of rolling a 2 would be (drum roll please).. 1 in 20.
If you're saying 'I've got a d20. The next roll will be an even number. What are the odds of that number being a 2?' Then I'd have to say the odds are 1 in 10. But how does one guarantee that no odd number will be rolled?
I'm thinking CJ/CIS is Criminal Justice/Criminal Information Systems.
If you're saying 'I've got a d20. The next roll will be an even number. What are the odds of that number being a 2?' Then I'd have to say the odds are 1 in 10. But how does one guarantee that no odd number will be rolled?
It's a conditional probability problem. It's guaranteed because the question says it's guaranteed. It's a math question, not a physics question.
My HS world geography teacher was a sadistic guy. He put patterns into all his tests, but he also rotated the correct answers. So my 100% score could go a,b,c,d,a,b,c,d.. while my friend could have the same answers but need to respond d,c,b,a,d,c,b,a.. Made colluding and/or selling answers a real pain.
Craps Probabilities
Craps Conditional Probability Rules
I'm sorry, fellas. The numbers on the dice are 1-20. My understanding of this questions is, what is the probability you will roll an even number and what is the probability that even number will be 2? The next question on the test is 'Find the probability of drawing a king given that you draw a spade.' I'm pretty sure both questions require the same method to solve.
CJ - Criminal Justice
The numbers on the 20 sided dice are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. If this reply sounds smartalically, I appologize. I don't really understand what you mean needing to 'specify what's on the 20-sided die.' Anyhow, which is the answer; a, b, c, or d?
There are 10 even numbers. If you know for sure that it is even, then the answer is 1/10.
You can also solve this by going through the formula for conditional probability. To be honest I always have to look it up (check wikipedia for conditional probability), but you will end up dividing 1/20 by 10/20 and get 1/10.
'But how does one guarantee that no odd number will be rolled?' Probable probability.
Thank you.
1.4-13 Tn the gambling game 'craps' a pair of dice is rolled and the outcome of the experiment is the sum of the points on the up-sides of the six-sided dice. The bettor wins on the first roll if the sum is 7 or 11. The bettor loses on the first roll if the sum is 2, 3, or 12. If the sum is 4, 5, 6, 8, 9, or 10, that number is called the bettor's 'point.' Once the point is established, the rule is, If the bettor rolls a 7 before the 'point,' the bettor loses; hut if the 'point' is rolled before a 7, the bettor wins.
(a) List the 36 outcomes in the sample space for the roll of a pair of dice. Assume that each of them has a probability of 1/36.
(b) Find the probability that the bettor wins on the first roll. That is, fInd the probability of rolling a 7 or ii, P(7 or 11).
(c) Given that 8 is the outcome on the first roll, find the probability that the bettor now rolls the point 8 before rolling a 7 and thus wins. Note that at this stage in the game the only outcomes of interest are 7 and 8. Thus find P(8 | 7 or 8).
(d) The probability that a bettor rolls an 8 on the first roll and then wins is given by P(8)P(8 | 7 or 8). Show that this probability is (5/36)(5/11).
(e) Show that the total probability that a bettor wins in the game of craps is 0.49293.
HINT: Note that the bettor can win in one of several mutually exclusive ways: by rolling a 7 or ii on the first roll or by establishing one of the points 4, 5, 6. 8, 9, or 10 on the first roll and then obtaining that point before a 7 on successive rolls.
https://brainmass.com/math/probability/conditional-probability-gambling-146405
Attachments
Conditional Probability Formula
Conditional probability is investigated. The solution is detailed and well presented. The response received a rating of '5/5' from the student who originally posted the question.
