Mindscapes for Chapter 7.1 & 7.2 please post original response by Friday 11/12(noon) and classmate responses by Sunday 11/14 (noon). If you need to post a drawing or handwritten work and do not have the capability to scan it as a .jpeg it must be submitted to my mailbox (Basement of AB building) by noon on Thursday and I will post in on Friday:
7.1 1) [JTL]You walk into a room with 20 spinning pennies how many will land tails up or heads up when done spinning? There will be about 10 each. 7.1 2) [CSV]; Wow! This question is making my head hurt! =P So, how many people would we need in a room so that the chance that two or more of them share a birthday is over 50%? I would guess that it would have to be 182ish. Because that is around half of the days of the year? But I'm only guessing. I'm almost positive that that is wrong! So yeah that question is quite confusing. We at least know that it won't be 367 because that guarantees at least 2 people will have the same birthday so its 100%. So cutting that in half would be the first instinct. But the percenctage is too high. It does say that you need only 23 people to achieve the 50% chance how the math works im not quite sure.~Uraqtinvu 7.1 3) [FAB]: 47% of the coins will be tails if 53 out of 100 are heads. CHRIS: Yeah! That pretty much makes sense
7.1 4) [TRC] I'm not sure if this is right because the book did not clearly state how to figure this out but I got 56% for heads and 44% for tails. 7.1 5) [SMD]:What percentage of children have their birthdays in December? A:3/12 In February? A:0% there was no one with a birthday in this month What percentage have their birthdays in the same month as another child at the party? A: 5/12 7.1 6) [NMG] I am not sure if I was suppose to do this with 100 pennies or what so I did it with a penny. 59=heads, 41=tails. 59% heads
7.1 7) [MRH] Flipping Lincoln: Flip a penny 100 times and see how they land. Record your results. What percentage of the pennies landed heads up? Answer: My boyfriend and I each tried this one so I would have two trials. Trial 1: 27 heads, 73 tails. So the percentage of heads would be 27%. (This was his, and quite unexpected results) Trial 2: 47 heads, 53 tails. So the percentage of heads would be 47%.
Comment (SMD) i'ts interesting that yours was some what around the same number and his was really high with tails.
CHRIS: That is odd. I would have expected it to be more around equal. Your second trial was good, but the first one is so drastically leaning.
Loreen: I ended up with 64 tails and 27 heads.
7.1 8) [JEH] I flipped the penny 100 times and it landed heads up 58 times out of 100, I don't understand why this is in these problems though, there is nothing to solve for whatsoever 7.1 9) [LJJ] Well I picked the King 82% of the time comment KLK: Our problems were really similar.. I did yours too & I ended up picking the king more than with mine! comment SMD: That happend with me when I tried the problem also! LJJ Yeah I did it with my daughter too and almost identical results.
7.1 10) [KLK] At first, I was horrible at picking the king.. but after 50ish times, I ended up choosing the king about 75%.
7.2 2) [JTL] 7.2 3) [CSV] We have: three red four yellow two green five blue candies in a bag. If I pull one out, what is the probability it is green? blue? That I will eat it?
Altogether there are 14 pieces of candy. there are two greens, so that makes it 2/14? which is narrowed down to 1/7th. blue would be 5/14. which can't be simplified anymore. I'm pretty sure I would eat it. 100%? That seems to be right. And yes it is definately 100% that you will eat it. For me probably 50% depends if im craving candy because i don't like chocolate covered candy. But if i am craving candy i'd probably eat it. Hehehe.~Uraqtinvu 7.2 4) [FAB]: 59/75= .78666 or 77% 11/75= .147 or 15% and 5/75= .06666 or 6.7% 7.2 5) [TRC]describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed. 7.2 12) [SMD]: What is the probability of rolling a 7 or 11 with two fair dice? Answer: 2/9. I got this because there are six ways to roll a 7 with fair dice and 2 ways to roll an 11 giving you 8/36 which is then changed to 2/9. CHRIS: Maybe I'm just being weird, but shouldn't it be higher? 7 is about the most common number rolled with two dice. Maybe 11 would jog it down a bit, but that much? Once again, I'm probably thinking incorrectly 7.2 13) [NMG]The probabilty of getting a heads and a 4 is 1/12. Looking at the table there are 12 different possible combinations that can be rolled therefore there is a 1/12 chance of getting heads & 4. If someone rolls the dice and gets a 2 there is a 1/2 (50%) chance that the dime is tails. If you look at where the dice rolls 2 in the table the only options are for 2 to be accompanied by a heads or a tails hence the 1/2 chance.
Possibilties
Dime
Dice
1.
Heads
1
2.
Tails
1
3.
Head
2
4.
Tails
2
5.
Heads
3
6.
Tails
3
7.
Heads
4
8.
Tails
4
9.
Heads
5
10.
Tails
5
11.
Heads
6
12.
Tails
6
7.2 14) [MRH] Suppose you have 10 marbles. They are each marked with one number: 1,2,3,4,5,6,7,8,9, or 10. They are placed in a jar, and you reach in and select one. Question 1: What is the probability that the number you select has a factor of 3? Answer: 3/10 = 30% Question 2: What is the probability that the number you select is a prime number? Answer: 4/10 = 2/5 = 40% Question 3: What is the probability that the number you select is even? Answer: 5/10 = 1/2 = 50% Question 4: What is the probability that the number you select is is evenly divisible by 13? Answer: 0/10 = 0%
7.2 15) [JEH] The probably is rolling a Roosevelt and a 4 is 1/12, and the probability of the one coin showing tails after being flipped is 1/2 because it could only be either heads or tails 7.2 18) [LJJ] 34% chance of landing on 13 and 47% chance of landing on a red spot MRH003 Comment: I got the same answer for the chances of landing on a red spot, but I think I may have interpreted the first part wrong because I got a 2% chance of landing on 13. How did you get your answer? LJJ: No your right I was looking at another problem Opps...
7.1 1) [JTL]You walk into a room with 20 spinning pennies how many will land tails up or heads up when done spinning? There will be about 10 each.
7.1 2) [CSV]; Wow! This question is making my head hurt! =P So, how many people would we need in a room so that the chance that two or more of them share a birthday is over 50%? I would guess that it would have to be 182ish. Because that is around half of the days of the year? But I'm only guessing. I'm almost positive that that is wrong!
So yeah that question is quite confusing. We at least know that it won't be 367 because that guarantees at least 2 people will have the same birthday so its 100%. So cutting that in half would be the first instinct. But the percenctage is too high. It does say that you need only 23 people to achieve the 50% chance how the math works im not quite sure.~Uraqtinvu
7.1 3) [FAB]: 47% of the coins will be tails if 53 out of 100 are heads.
CHRIS: Yeah! That pretty much makes sense
7.1 4) [TRC] I'm not sure if this is right because the book did not clearly state how to figure this out but I got 56% for heads and 44% for tails.
7.1 5) [SMD]:What percentage of children have their birthdays in December? A:3/12
In February? A:0% there was no one with a birthday in this month
What percentage have their birthdays in the same month as another child at the party? A: 5/12
7.1 6) [NMG] I am not sure if I was suppose to do this with 100 pennies or what so I did it with a penny. 59=heads, 41=tails. 59% heads
7.1 7) [MRH] Flipping Lincoln: Flip a penny 100 times and see how they land. Record your results. What percentage of the pennies landed heads up?
Answer: My boyfriend and I each tried this one so I would have two trials.
Trial 1: 27 heads, 73 tails. So the percentage of heads would be 27%. (This was his, and quite unexpected results)
Trial 2: 47 heads, 53 tails. So the percentage of heads would be 47%.
Comment (SMD) i'ts interesting that yours was some what around the same number and his was really high with tails.
CHRIS: That is odd. I would have expected it to be more around equal. Your second trial was good, but the first one is so drastically leaning.
Loreen: I ended up with 64 tails and 27 heads.
7.1 8) [JEH] I flipped the penny 100 times and it landed heads up 58 times out of 100, I don't understand why this is in these problems though, there is nothing to solve for whatsoever
7.1 9) [LJJ] Well I picked the King 82% of the time
comment KLK: Our problems were really similar.. I did yours too & I ended up picking the king more than with mine!
comment SMD: That happend with me when I tried the problem also!
LJJ Yeah I did it with my daughter too and almost identical results.
7.1 10) [KLK] At first, I was horrible at picking the king.. but after 50ish times, I ended up choosing the king about 75%.
7.2 2) [JTL]
7.2 3) [CSV] We have:
three red
four yellow
two green
five blue
candies in a bag. If I pull one out, what is the probability it is green? blue? That I will eat it?
Altogether there are 14 pieces of candy. there are two greens, so that makes it 2/14? which is narrowed down to 1/7th. blue would be 5/14. which can't be simplified anymore. I'm pretty sure I would eat it. 100%?
That seems to be right. And yes it is definately 100% that you will eat it. For me probably 50% depends if im craving candy because i don't like chocolate covered candy. But if i am craving candy i'd probably eat it. Hehehe.~Uraqtinvu
7.2 4) [FAB]: 59/75= .78666 or 77% 11/75= .147 or 15% and 5/75= .06666 or 6.7%
7.2 5) [TRC] describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.
7.2 12) [SMD]: What is the probability of rolling a 7 or 11 with two fair dice? Answer: 2/9. I got this because there are six ways to roll a 7 with fair dice and 2 ways to roll an 11 giving you 8/36 which is then changed to 2/9.
CHRIS: Maybe I'm just being weird, but shouldn't it be higher? 7 is about the most common number rolled with two dice. Maybe 11 would jog it down a bit, but that much? Once again, I'm probably thinking incorrectly
7.2 13) [NMG] The probabilty of getting a heads and a 4 is 1/12. Looking at the table there are 12 different possible combinations that can be rolled therefore there is a 1/12 chance of getting heads & 4. If someone rolls the dice and gets a 2 there is a 1/2 (50%) chance that the dime is tails. If you look at where the dice rolls 2 in the table the only options are for 2 to be accompanied by a heads or a tails hence the 1/2 chance.
7.2 14) [MRH] Suppose you have 10 marbles. They are each marked with one number: 1,2,3,4,5,6,7,8,9, or 10. They are placed in a jar, and you reach in and select one.
Question 1: What is the probability that the number you select has a factor of 3? Answer: 3/10 = 30%
Question 2: What is the probability that the number you select is a prime number? Answer: 4/10 = 2/5 = 40%
Question 3: What is the probability that the number you select is even? Answer: 5/10 = 1/2 = 50%
Question 4: What is the probability that the number you select is is evenly divisible by 13? Answer: 0/10 = 0%
7.2 15) [JEH] The probably is rolling a Roosevelt and a 4 is 1/12, and the probability of the one coin showing tails after being flipped is 1/2 because it could only be either heads or tails
7.2 18) [LJJ] 34% chance of landing on 13 and 47% chance of landing on a red spot
MRH003 Comment: I got the same answer for the chances of landing on a red spot, but I think I may have interpreted the first part wrong because I got a 2% chance of landing on 13. How did you get your answer?
LJJ: No your right I was looking at another problem Opps...