Problem 4. Five coins are flipped. The first four coins will land on heads with probability...
13. What is the probability for exactly three of five flipped coins to land heads, and in how many different ways can they land to give this result?
Answer part a and part b please!!! (a) What is the conditional probability that exactly four Tails appear w when a fair coin is flipped six times, given that the first flip came up Heads? (I.e. the coin , then is flipped five more times with Tails appearing exactly lour times.) (b) What if the coin is biased so that the probability of landing Heads is 1/3? (Hint: The binomial distribution might be helpful here.) (a) What is the conditional...
when coin 2 is flipped it lands on heads with When coin 1 is flipped, it lands on heads with probability probability (a) If coin 1 is flipped 12 times, find the probability that it lands on heads at least 10 times. (b) If one of the coins is randomly selected and flipped 9 times, what is the probability that it lands on heads exactly 6 times? (c) In part (b), given that the first of these 9 flips lands...
You have five coins in your pocket. You know a priori that one coin gives heads with probability 0.4, and the other four coins give heads with probability 0.7 You pull out one of the five coins at random from your pocket (each coin has probability 릊 of being pulled out), and you want to find out which of the two types of coin it is. To that end, you flip the coin 6 times and record the results X1...
Problem 1. A biased coin with probability plandin with a Heads is lipped 4 times. (a) Define the basic random variables and give the sample space and assign probabilities to the outcomes. (b) Let X be the total number of Heads in the four flips Draw a Venn diagrain showing the five events X = ii 0,1,2,3,4 as well as the sample space and the outcomes. Is X a random variable? c) Are the events X 1 and X 2...
Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probability 0.5 and tails with probability 0.5) and one is a trick coin which alwavs flips heads. Renata the Fox skillfully robs Mysterioso of one of the coins in his box (chosen uniformly at random). She decides she will flip the coin k times to test if it is the trick coin. (a) What is the...
Problem 1 (5 points) A coin is flipped four times. Assume that each of the sixteen possible outcomes {0000, 1000, 0100, 1100, 0010, 1010, 0110, 1110, 0001, 1001,0101, 1101,0011, 1011, 0111, 1111} are equally likely. What is the conditional probability that all flips are heads, given the following information: (a) the first flip is heads? (b) the last flip is heads? (©) at least one flip is heads? (d) at least two flips are heads? (e) the first flip and...
A box contains four coins. Three of the coins are fair, but one of them is biased, with P(11) = ? (where 11 is the event of flipping heads). You take a coin from the box and flip it. It comes up heads. What is the probability that you have flipped the biased coin?
2. Mysterioso the Magician is walking down the street with a box containing 25 identical looking coins: 24 are fair coins (which flip heads with probabilty 0.5 and tails with probability 0.5) and one is a trick coin which always flips heads. Renata the Fox skillfully robs Mysterioso of one of the coins in his box (chosen uniformly at random). She decides she will flip the coin k times to test if it is the trick coin (a) What is...
Assume that a coin is flipped where the probability of coin lands "Heads" is 0.49. The coin is flipped once more. This time, the probability of obtaining the first flip's result is 0.38. The random variable X is defined as the total number of heads observed in two flips. On the other hand, the random variable Y is defined as the absolute difference between the total number of heads and the total number of tails observed in two flips. Calculate...