Dan and Ella are paying $4 to play a game at the school carnival. Ella is blindfolded. Dan is given 7 coins to place in 2 different cups. He is given 4 pennies and 3 gold coins (identical in size). He randomly arranges them in the two cups in any combination he chooses. Ella is now instructed to choose a coin randomly out of one of the cups. If she chooses a gold coin, they win $20. If they choose a penny, they do not win anything. What is the probability that Ella will choose the gold coin in all possible situations ( I want a different probability for each situation)? Which combination would be BEST for Dan to choose when placing the coins in the cup? Which would be the worst?
The best order to put it in is the PPPP/GGG because it is a one half chance and if you pick the right one you win, but if you pick the wrong one then you lose so it is a fifty fifty chance. The one order you don’t want is the PPPGGG/P. this is the worst one because if you pick the one with a penny in it you lose right away. But if you pick the other one you have a ½ chance because there is the same amount of coins. Three pennies, three gold coins. So this is the worst one.
ReplyDeleteThe best combination for Dan to choose when arranging the coins is PPPPGG/G. This combination will give Ella the greater probability of winning because after making each area model and finding each probability of all the individual combinations, PPPPGG/G had the highest percent after adding up all the fractions. The probability of Ella picking a gold coin from this combination is 2/3. 2 divided by 3 is .6 repeating, giving her the highest number compared to the rest of the combinations. However, the worst combination for Dan to choose is P/PPPGGG. After creating the area model and finding the probability for this combination, which was 3/12, 3 divided but 12 was .25 giving you the lowest probability.
ReplyDeleteThe best combination for Dan to choose is PPPPGG/G. This combination has the greatest probability of winning because after finding each probability of all the possible combinations, PPPPGG/G had the highest percent after adding up all the fractions. The probability of Ella picking a gold coin from this combination is 2 out of 3. 2 divided by 3 is .6 repeating, which is the largest number out of all of the other ones. The combination with the worst probability is P/PPPGGG. After finding the probability for this combination, which was 3 out of 12, and 3 divided by 12 was .25 which was the lowest number, giving you the lowest probability.
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ReplyDeletethe best combonation is pgg/pppg
ReplyDeleteThe best choice would be pppp in cup 1 and ggg in cup 2 because you have a 50% of picking the cup with the gold coins. The worst would be pppp in cup 1 and ggg in cup 1 as well because the other cup is empty and then you haft to pick the right coin.
ReplyDeleteThe best combination is cup one: GG/cup two: PPPPG, this is because it gives u probability because it gives you a probability of 3/5. The worst combination is cup one: GGGPPPP/cup two: EMPTY, this is because the probability of get a gold coin is 3/14.
ReplyDeleteFor this problem the best combination would be G/PPPPGG. The reason is because at the start you have a 1 half chance of winning. If you pick the one with the one gold coin you win on the spot. Having more than 1 gold coin in that bucket would only lower your chances in the other cup. Having two gold coins in one cup does you no good, so leave just one in that cup. Then put the 2 last gold coins in the other cup along with the four pennies. This will raise your chances in winning in that cup. Putting 1 penny in the cup with only one gold coin will give you a 1 half shot of winning so that would lower your chances in that cup. having the combination P/PPPGGG is the worst one. This is because in one cup you have a 100% chance of losing and in the other only a half shot of winning. This is by far the worst cup to have. Dan should choose G/PPPPGG.
ReplyDeleteI would say Dan should go with gold in 1 gold in 1 cup and 2 golds and 4 pennies in cup 2 because you have a greater possibility of getting a gold coin. Dan should not go with the cup 1 empty and in cup 2 have 3 gold’s and 4 pennies because you have one cup that is empty and you think that the empty cup has a least on 1 penny or 1 gold.
ReplyDeleteThe best combination for picking a gold coin would be g/ggppp. This is because you would have 1 cup with 1 gold coin, which would be 1/2 of the probability already. Also, in the other cup, there would be a 2/5 chance of getting the gold coin.
ReplyDeleteThe worst combination for picking a gold coin would be p/pppggg. P would be in one cup which would already be half of the probability of picking a gold coin. In the other cup there would be another 1/2 chance of picking a penny.
The best combination is PPPPG/G because it has the highest probability of getting all three gold coins is 2/3 which is the highest fraction out of all 10 and the best way for Ella to win the game. The worst combination is P/PPPGGG because the fraction is 1/4 and that is the lowest.
ReplyDeleteThe best combination is PPPP/GGG which gives you a ½ chance of getting gold. The worst combonation is GPP/PPGG which gives you 1/8 of getting gold.
ReplyDeleteThe best combination would be putting a Gold coin in one container, and having the four pennies, and the other two gold coins in the other container. This would be the best option because it gives you a 66.7% chance of getting the gold coin.
ReplyDeleteThe worst combination would be putting all 7 coins in one container, and leaving the second container empty. This would be a bad decision because it only gives you a 21.4% chance of winning. Compared to the other 9 combinations, this combination had the lowest probability.
The best combination for Dan to choose when arranging the coins is ppppgg/g, because this will give Ella the highest probability of picking a winning combination. After I did all of my work and all of the area models I found out that this was the highest probability. The probability of Ella picking this coin is 2/3 which was the greatest when compared to the rest of the combination. The worst combination that Dan could put together is P/gggppp because it had the lowest probability of 3/12 which is the lowest probability when compared to the other individual probabilities.
ReplyDeleteThe best arrangement is going to be putting ppppgg in one cup and in the other cup put g. the p(g) is 2/3 far greater than the other prob. The worst arrangement is putting ppppggg/___ the p(g) is 3/14. This has the smallest chance of winning.
ReplyDeleteI think the best answer is PPGG in container 1, and PPG in container 2. Because when you add the fractions in order they don’t have the same common denominator. So you need to change them to a 6 and you add them. You gat 6/6 which is one hole. The worst possible answer is empty in container 1 and all of them in container 2. And for your answer you get 3/14 and the percent 5.
ReplyDeleteThe best combination for this problem would be in the first cup (GGG) and the second (PPPP) after doing the area model I found out that you will have a ½ or 50% chance of picking the cup with all Gold Coins. Then if you pick that cup then well automatically win because there are all Gold Coins in the cup!
ReplyDeleteThe worst combination would be in the first cup you will have (P). Then in the second cup you will have (PPPGG). After doing the area model I found out that you will have a ¼ or 25% chance of getting the gold coin and winning! Because you have a 50% chance of picking the cup with the Gold Coin, but only one cups has some Gold Coins in it but if you pick that cup you will only have a 2/5 chance of getting a Gold Coin out of that cup.
The best combination is ppppg/gg. That is the best combo because you have a better chance of getting a gold coin if he chooses the right cup he would have a 100% chance of winning. The least chance of winning is p/gggppp. After finding the probability for this combination, which was 3 out of 12, and 3 divided by 12 was .25 which was the lowest number, giving you the lowest probability.
ReplyDeleteI think it is pgg/pppg when i also think the wors one is pppggg/g it is only i/4 witch is only 20% chans
ReplyDeleteThe best combontion for picking a gold coin is ppp/ggg because you add 1/8 + 3/6 then you get 1 half which is the highest nimber i got. Also when you didvied it in an area model the p's are didvided in to 8th and the g's are divided into 6ths. The Worst one is pppp/ggg because you will only have a 50% chance of getting a gold coin. Which ever cup you chose you will eather get a win or a lose. some of the other combonations have where there are good amount of each coins in each cup so you will have a better chance of winning.
ReplyDeleteThe best choice is… P,P,P,P, G,G/G
ReplyDeleteBecause it simplified = (6/12+1/12+1/12= 8/12) = 2/3
The worst choice is… P,P,P,P,G,G,G/ empty
Because it simplified = (1/14+1/14+1/14) = 3/14
The best combination Dan can pick is cup 1 has one gold coins, and then cup 2 has four pennies in it. It is the best on because the probability of the gold coins is 2/3 because he has a better chance of winning. The worst combination is in cup 1 there is 1 penny; then in cup 2 there is 3 pennies, and 3 gold coins, and the probability of the gold coins is 1/4. It is the worst because he will have a less chance of winner.
ReplyDeleteThe best combination would be PPPP/GGG because you would have a half chance of winning. But the worst combination would be PPPPGGG/EMPTY because since CUP 2 is empty you would have to pick from CUP 1 which has all the coins. And you would have a 3/14 chance of winning.
ReplyDeleteThe best order arrange the coins in to have the best chance to pick a gold coin is to put all of the gold coins in 1 cup and all of the pennies in the other cup because the probability to pick a gold coin and win is ½ . The arrangement that will least have a gold coin to picked is to put 2 gold coins and 1 penny in one cup and 3 pennies and 1 gold coin in the other cup because the probability to pick a gold coin is 5/24 which is a very unlikely chance to pick a gold coin and win.
ReplyDeleteFor this question the best answer in my opinion I think the best combination would be 1 gold in cup 1 and 2 gold’s and 4 pennies in cup 2. This is best because you have a greater probability of pulling out gold in that one. This is the best choice because of the probability is 2/3 as the other option has a lower probability.
ReplyDeleteThe best order for Dan to choose is PPPP/GGG because you have a 50 percent chance of getting the gold coin. The worst possibility is GPP/PPG because you have a 16 percent chance to get the gold coin.
ReplyDelete