Question 4 (20 points) A box contains three coins, two fair coins and one two-headed coin....
a bag contains one fair coin, two two-headed coins, and three two-tailed coins. each of the is flipped, but the outcomes of the fice coins are hidden from you, randomly. if the outcome you see is headsm, what is the probability that the fair coin (which may or may not be the coin that was shown to you) panded heads up?
You have 2 fair coins and one coin with heads on both sides. You pick a coin at random and toss it twice. If it lands heads up on both tosses, the probability it also lands heads up on a third toss can be express in the form A/B, where A and B are relatively prime positive integers (i.e. the greatest common divisor is 1). Compute A + B.
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?
A jar contains 100 coins, where 99 are fair, but one is double-headed (always landing heads). A coin is chosen randomly from the jar. Then, the chosen coin is flipped 5 times. (a) Compute the probability that the coin lands heads all 5 times. (b) Given the coin lands heads all 5 times, what is the probability that the chosen coin is double-headed?
Suppose there are two coins. One is a standard fair coin, so that P(heads)=0.50. The other one is a two-sided coin, so that P(heads)=1. You draw one of the two coins at random and toss it. It results in heads. Given that observation... (a) Compute the probability that you have selected a fair coin. (1pt) (b) What is the probability that the next toss will result in heads too? (1pt) (c) If the next toss results in heads as well,...
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?
A box contains five coins. For each coin there is a different probability that a head will be obtained when the coin is tossed. (Some of the coins are not fair coins!) Let pi denote the probability of a head when the i th coin is tossed (i = 1, . . . , 5), and suppose that p1 = 0, p2 =1/4, p3 =1/2, p4 =3/4, p5 =1. The experiment we are interested in consists in selecting at random...
Problem 6 A box contains 4 coins: • coin 1 has both sides heads. • coin 2 has both sides tails. • coin 3 has both sides tails. • coin 4 is a regular coin (1 side head, other side tails). (a)(3 points) If we randomly choose one coin from the box and flip, what is the probability we get heads? (b)(3 points) If we randomly choose one coin, flip, and it comes up heads, what is the probability it...
Question 1 [20 points] We are given three coins: one has heads in both faces, the second has tails in both faces, and the third has a head in one face and a tail in the other. We choose a coin at random, toss it, and the result is heads. What is the probability that the opposite face is tails?
You have in your pocket two coins, one bent (comes up heads with probability 3/4) and one fair (comes up heads with probability 1/2). Not knowing which is which, you choose one at random and toss it. If it comes up heads you guess that it is the biased coin (reasoning that this is the more likely explanation of the observation), and otherwise you guess it is the fair coin. A) What is the probability that your guess is wrong?