I'm not sure the reasoning for question 5 is valid. I don't think the proposed definition of Kevin beats Jim as "P(white) - P(green)" is correct. The question is slightly ambiguous as it does not specify whether landing on either colour results in a re-spin, so I'll cover both cases below. (I would probably assume that landing on another colour results in a respin, but regardless, it's probably a good idea to specify: "The players keep spinning until a player wins" or something similar for further clarity.) If we assume that the spinner landing on another colour results in a re-spin, then the P(Kevin beats Jim) = P(White appears before green). In this case, we can simply ignore the respins/other colours, as they do not affect the eventual outcome. This leaves P(Kevin beats Jim) as (Proportion which is white) / (Proportion which is white or green), leaving options A and C as being equally correct. (Both a 2/3 chance of Kevin winning). Their relative sizes don't actually matter, they simply determine how long the game will take to conclude. If we assume that the spinner landing on another colour results in a draw/game finish where neither player wins, then P(Kevin beats Jim) = P(Kevin wins after one spin) = P(White), leaving options A and B as being equally correct, at 50% A is the safest answer, as it satisfies both requirements, but in neither case is it strictly correct.
Just like Gavin said. I think it's little bit over complicated in the video. The question basically says: "which wheel gives white the greatest chance of BEATING green?" Obviously it's wheel A) because White has to BEAT green in order to win. 50% chance is higher than 40%. Tie is NOT a favourable result in this scenario.
For Gavin and Juboy, as George said before, in the cases you gave, answer B would also suffice (his forth paragraph). A way to ask the question so answer "A" is the only correct answer would be: Which option gives Kevin the best chance to win and Jim the lowest chance. (for example) In my opinion (judging by the difficulty of the rest of the test), this question should have either had more obvious answers (in which case you should just remove it), or put in as a bonus question with better wording (like which wheel would be best for Kevin to choose, the answer would always be A, and I believe this would make for a nice bonus question for the students who understand probability and took the time to try and figure out the answer) Hope this will help anyone at all... and thanks George for saving me some time by explaining it yourself.
This is actually a very interesting question when you approach it with different goals in mind. What if you wanted to win more than your friend? (Fractions chosen for clarity.) A) Chance to spin white: 10/20 Chance to spin green: 5/20 Difference: 50% vs 25% C) Chance to spin white: 8/20 Chance to spin green: 4/20 Difference: 40% vs 20% In other words, in 100 spins, wheel A) has white win 25 more times whereas wheel C) has white win 20 more times. If you try the opposite approach and try to delay your friend for as long as possible, this is what happens: A) Chance to *not* spin white: 1/2 = 50% Chance to *not* spin green: 3/4 = 75% Chance to *not* spin white 5 times in a row: 0.5^5 = 0.03 = 3% In reverse: 97% of the time you spin white at least once in 5 attempts. Chance to *not* spin green 5 times in a row: 0.75^5 = 0.24 = 24% In reverse: 76% of the time you spin green at least once in 5 attempts. C) Chance to *not* spin white: 3/5 = 60% Chance to *not* spin green 4/5 = 80% Chance to *not* spin white 5 times in a row: 0.6^5 = 0.08 = 8% In reverse: 92% of the time you spin green at least once in 5 attempts. Chance to *not* spin green 5 times in a row: 0.8^5 = 0.33 = 33% In reverse: 67% of the time you spin green at least once in 5 attempts. C) is already pulling ahead. Let's continue. How long does it statistically take until you have a 100% chance to win at least a single time in all the unlucky attempts leading up to that point? A) Chance to *not* spin white in 8 tries: 0.5^8 = 0.004 Chance to *not* spin green in 19 tries: 0.75^19 = 0.004 C) Chance to *not* spin white in 11 tries: 0.6^11 = 0.004 Chance to *not* spin green in 25 tries: 0.8^25 = 0.004 So, while in A) you potentially win in fewer attempts than in C), it would take your friend longer to win at least once in C) than it would in A).
The teachers reasoning is actually incorrect. The question asked is what spinner should he pick so he has the highest probability of winning. This is simply the biggest fraction that is white; so in the first spinner he beats him 1/2, which is still the biggest but if a different spinner had 51% white and 49% green he still beats him more often on that 1/2 spinner even though the ratio is much smaller. If one respins if it’s not on green or white then 1 and 3 are equal. 1/2 - 1/4 or 2/5 -1/5 answers what spinner has the greatest difference in percentage points, which wasn’t asked. 25% > 20%.
I'm not sure the reasoning for question 5 is valid. I don't think the proposed definition of Kevin beats Jim as "P(white) - P(green)" is correct.
The question is slightly ambiguous as it does not specify whether landing on either colour results in a re-spin, so I'll cover both cases below. (I would probably assume that landing on another colour results in a respin, but regardless, it's probably a good idea to specify: "The players keep spinning until a player wins" or something similar for further clarity.)
If we assume that the spinner landing on another colour results in a re-spin, then the P(Kevin beats Jim) = P(White appears before green). In this case, we can simply ignore the respins/other colours, as they do not affect the eventual outcome. This leaves P(Kevin beats Jim) as (Proportion which is white) / (Proportion which is white or green), leaving options A and C as being equally correct. (Both a 2/3 chance of Kevin winning). Their relative sizes don't actually matter, they simply determine how long the game will take to conclude.
If we assume that the spinner landing on another colour results in a draw/game finish where neither player wins, then P(Kevin beats Jim) = P(Kevin wins after one spin) = P(White), leaving options A and B as being equally correct, at 50%
A is the safest answer, as it satisfies both requirements, but in neither case is it strictly correct.
Just like Gavin said. I think it's little bit over complicated in the video. The question basically says: "which wheel gives white the greatest chance of BEATING green?" Obviously it's wheel A) because White has to BEAT green in order to win. 50% chance is higher than 40%. Tie is NOT a favourable result in this scenario.
For Gavin and Juboy, as George said before, in the cases you gave, answer B would also suffice (his forth paragraph).
A way to ask the question so answer "A" is the only correct answer would be: Which option gives Kevin the best chance to win and Jim the lowest chance. (for example)
In my opinion (judging by the difficulty of the rest of the test), this question should have either had more obvious answers (in which case you should just remove it), or put in as a bonus question with better wording (like which wheel would be best for Kevin to choose, the answer would always be A, and I believe this would make for a nice bonus question for the students who understand probability and took the time to try and figure out the answer)
Hope this will help anyone at all... and thanks George for saving me some time by explaining it yourself.
This is actually a very interesting question when you approach it with different goals in mind. What if you wanted to win more than your friend? (Fractions chosen for clarity.)
A)
Chance to spin white: 10/20
Chance to spin green: 5/20
Difference: 50% vs 25%
C)
Chance to spin white: 8/20
Chance to spin green: 4/20
Difference: 40% vs 20%
In other words, in 100 spins, wheel A) has white win 25 more times whereas wheel C) has white win 20 more times.
If you try the opposite approach and try to delay your friend for as long as possible, this is what happens:
A)
Chance to *not* spin white: 1/2 = 50%
Chance to *not* spin green: 3/4 = 75%
Chance to *not* spin white 5 times in a row: 0.5^5 = 0.03 = 3%
In reverse: 97% of the time you spin white at least once in 5 attempts.
Chance to *not* spin green 5 times in a row: 0.75^5 = 0.24 = 24%
In reverse: 76% of the time you spin green at least once in 5 attempts.
C)
Chance to *not* spin white: 3/5 = 60%
Chance to *not* spin green 4/5 = 80%
Chance to *not* spin white 5 times in a row: 0.6^5 = 0.08 = 8%
In reverse: 92% of the time you spin green at least once in 5 attempts.
Chance to *not* spin green 5 times in a row: 0.8^5 = 0.33 = 33%
In reverse: 67% of the time you spin green at least once in 5 attempts.
C) is already pulling ahead. Let's continue. How long does it statistically take until you have a 100% chance to win at least a single time in all the unlucky attempts leading up to that point?
A)
Chance to *not* spin white in 8 tries: 0.5^8 = 0.004
Chance to *not* spin green in 19 tries: 0.75^19 = 0.004
C)
Chance to *not* spin white in 11 tries: 0.6^11 = 0.004
Chance to *not* spin green in 25 tries: 0.8^25 = 0.004
So, while in A) you potentially win in fewer attempts than in C), it would take your friend longer to win at least once in C) than it would in A).
The teachers reasoning is actually incorrect. The question asked is what spinner should he pick so he has the highest probability of winning. This is simply the biggest fraction that is white; so in the first spinner he beats him 1/2, which is still the biggest but if a different spinner had 51% white and 49% green he still beats him more often on that 1/2 spinner even though the ratio is much smaller. If one respins if it’s not on green or white then 1 and 3 are equal. 1/2 - 1/4 or 2/5 -1/5 answers what spinner has the greatest difference in percentage points, which wasn’t asked. 25% > 20%.
for B to be the answer, the question needs to state that: which spinner is correct to show that they have an equal chance to land on their colour
how is this yr10 its so easy
Bro it's a review
@@user-yy3xd4vl8s damn bro homie got 1.47 mil subs
why is this so easy??? i could get all the questions correct. must be an american test.
its the easiest topic. Its pretty much a review of earlier years.
Tum mere youtu pe vidio send kyu k r h #######