1. P

    coins and weight....with possible error in balance measure

    I have run thru this problem: We are given 1000 coins, each of which weights a natural number of grams , and a two-pan balance, measuring in grams the weight difference between the objects placed on two plates. The balance is generally reliable, but for a construction defect we know that at...
  2. C

    An investigation of piles of coins

    Hi all, this is my first post so apologies if this is in the wrong thread! I am well and truly stuck with this investigation and any help would be greatly appreciated. The question is: Start with two unequal piles of coins. Shift enough coins from the larger pile to the smaller pile, so that...
  3. J

    Probability of Coins Flips

    When I initially thought about the problem, I thought of it as if both had 4 coins, then they would on average get the same number of heads. If Person A had one more coin, then it would be a 50/50 shot for Person A to have more each time. But the more I think about this, its making less sense to...
  4. G

    Growth rate and regular coins, and one unfair coin.

    I'm completely lost on this one; I haven't encountered a question like this before (with two growth rates). So, there's this experimenter who tosses 4 coins (this is toss 1) and about half of them (2) land with heads up. She adds the amount that landed heads up (2) to the intial number of...
  5. B

    The 7 coins puzzle

    Someone says she has 7 coins, what is the probability that it is over $1? Spoiler: Probability Puzzles: The Seven Coins of James Bond
  6. U

    How do I arrange 6 coins to form a triangle with 4 coins on each side?

    Can anyone help me with this? Thanks in advance.
  7. T

    A puzzle problem involving coinage

    A shopkeeper and her customer each have an unlimited number of coins. However, they are of only two denominations – 3¢ and 5¢. 1. What amount purchases are not possible using only these two denominations of coinage, if the shopkeeper is allowed to give change back to the customer? 2. If...
  8. M

    combinatorics and coins

    If you toss 1000 fair coins 10 times each what is the probability that *some* coin will get 10 heads?
  9. K

    Pile of Coins

    100 Piles of Coins Hi all, I came across this problem: We have 100 piles of coins, with the ith pile containing exactly i coins. We wish to remove all the coins in a series of steps. In each step we are allowed to take away coins from as many piles as we wish, but we have to take the same...
  10. M

    Flipping coins

    I'm trying to write out the following Bernoulli Space events in terms of E_n \Omega = \{ \omega = \omega_1 \omega_2 \omega_3 \ldots : \omega_n = 1,0 \} (i) exactly 2 heads are obtained. E_x=\{ \omega \in \Omega : \omega_x=1 \} E_y=\{ \omega \in \Omega : \omega_y=1 \} E_z= \{\omega \in...
  11. A

    Question on weight of coins

    In this question: 1 pence coins weigh 3.5g 2 pence coins weigh 7g A bag contains a mixture of 2 pence and 1 pence coins. It is worth £2. What does it weight? I am a little stuck on this one, puzzled... Thanks for any help!
  12. N

    The 10 pirates and 100 gold coins problem

    10 very smart pirates sorted from high level to low level obtained 100 gold coins. The captain (the highest one) has to divide the 100 coins among all the people. If at least half of the people are satisfied with what they get, it's OK. If not, they will kill the captain and the second person...
  13. C

    Markov chain for tossing coins

    Question: A coin is tossed until five consecutive heads appear. Model this process as a Markov chain where the states are the numbers of consecutive heads. (0,1,...,5). a. Find the probability that it takes 10 or fewer tosses to observe five consecutive heads. b. Find the mean number of tosses...
  14. J

    Help with Proof: A cents in B coins --> B dollars in A coins?

    Hi, I need to solve this proof put I cannot seem to figure it out. I'd really appreciate some help! If a dollar is 100 cents and coins come in 1, 2, 5, 10, 20, 50 and 100 cents. Suppose that one can make A cents using exactly B coins. Prove that it is possible to make B dollars using exactly...
  15. R

    Find Coins of Each Type

    A collection of 50 coins is worth $5.20. There are twelve more nickes than dimes, and the rest of the coins are quarters. How many coins of each type are in the collection? This type of question always gives me a hard time. How do I set up the equation for coin problems?
  16. B

    I need help with my Probability Course assignment

    I have got a few questions for my assignment. I can't seem to solve 9 of these. I have no other way of getting help for these. I know these will come up for my exams. Please help me solve them.(Worried) 1. Suppose S is uncountable. Show that it is impossible that P({s}) > 0 for every s that...
  17. M

    Balancing Coins

    You have 22 coins which all weigh the same and 2 coins that are heavier than the rest, but equal in weight to each other. You have a balance that can compare two groups of coins. What is the smallest number of weighings necessary to find the two heavy coins?
  18. R

    Coins in a jar word problem

    I just joined today, thank you for making this forum. I will be coming here often, again thank you all so much. Here is the problem. The problem starts with coins in a jar and I must come up with the number of coins of each denomination. The number of quarters is unknown, number of dimes...
  19. L

    Coins Probability

    You have some coins in your pocket: 3 quarters, 2 dimes, and 4 pennies. What’s the probability that 3 coins taken randomly will be worth more than 50 cents?
  20. A

    tossing the two coins together, until for the first time either two heads appear ....

    Tom and Bob play a game by each tossing a fair coin. The game consists of tossing the two coins together, until for the first time either two heads appear when Tom wins, or two tails appear when Bob wins. 1) Show that the probability that Tom wins are or before the nth toss is \frac{1}{2} -...