5. Among eight coins there is one false coin which is lighter. You have a pan...
A friend of yours is given the following problem: You have 8 seemingly identical coins, among which you are told that one is a counterfeit. The counterfeit is known to be heavier than a true coin. You have access to a simple two-pan balance. What is the MINIMUM number of weighings you need to use in order to find the counterfeit coin? Your friend's answer is the following: I can identify the counterfeit coin by proceeding as follows: Weighing 1:...
You have 80 coins that are identical in appearance. Among them there are three fake coins and you know which ones. The genuine coins all have the same weight and the fake coins all have the same weight, but the fake coins are lighter than the real ones. Your friend knows that among the 80 coins there are either three or two fake coins. Without revealing the identity of any of the 80 coins, how can you use a pan...
a) In a collection of 900 coins, one is counterfeit and weighs either more or less than the genuine coins. Find a good lower bound on the number of balance scale weighings needed to identify the fake coin and determine whether it is too heavy or too light. Assume the balance scale has three states: tilted left, tilted right, or balanced. b)In a collection of 10 coins, 2 coins are counterfeit and weigh less than the genuine coins. Find a...
2. (10%) Suppose that among n identical-looking coins, one is fake. With a balance scale, we can compare any two sets of coins. That is, by tipping to the left, to the right, or staying even, the balance scale will tell whether the two sets weight the same, or which of the two sets is heavier than the other but not by how much. Please use the prune and search strategy to design an efficient algorithm for detecting the fake...
coin collector has a box that contains 125 unique coins. If you take a sample of six coins, how many different samples are possible? If eight of the coins in the box are from Denmark, how many samples of six coins contain exactly one coin from Denmark? How many samples of six contain at least one coin from Denmark?
1.13 (Counterfeit Coin Problem) We are given six coins, one of which is counterfeit and is known to have different weight than the rest. Construct a strategy to find the counterfeit coin using a two-pan scale in a minimum average number of tries. Hint: There are two initial decisions that make sense: (1) test two of the coins against two others, and (2) test one of the coins against one other.
Suppose you have two coins. One coin is fair and other is a coin with heads on both sides. Now you choose a coin at random and flip the coin. If the coin lands head, what is the probability that it was the fair coin?
You have 5 coins, four of which are fair coins, i.e. P(H)=P(T)= 0.5, and the other of which is a two headed coin, i.e. both sides have a head. Suppose you select a coin at random and flip in 3 times, getting all heads. If you flip the coin again, what is the probability it will be heads?
You have one fair coin and one biased coin which lands tails with probability 2/3. You pick one of the coins at random and flip it twice. It lands trails booth times. Given this information, what is the probably that the coin that you picked is the fair one?
I have two coins, one fair, and one unfair which shows heads ¾ of the time. I choose a coin at random and flip it 10 times. How many heads do I expect to see? Solve via conditional expectation.