will_you_be_alive_test 08-May-2019 15:53:40 will_you_be_alive_test MATLAB version Test will_you_be_alive. AIRPLANE_SEAT: Airline passengers 1 through N are assigned seats 1 through N. But passenger 1 is clueless, and chooses a seat randomly. The remaining passengers board in order, choosing their assigned seat if possible, otherwise taking an empty seat at random. What is the probability that the last passenger, N, will be able to sit in the correct assigned seat N? Estimated probability = 0.49 Theoretical probability = 0.5 BEFORE: Probability of flipping 4 heads before 7 tails. If probability of one head is 0.45, probability of success = 0.733814 If probability of one head is 0.5, probability of success = 0.828167 BLACK + DRAW: Draw one marble at a time from a bag of B black and W white marbles. What is the probability the last marble is black? Exact result is 1/2! 1 1 0.4973 1 10 0.5071 2 3 0.4972 3 3 0.5032 5 4 0.5058 7 9 0.5 18 13 0.4998 15 39 0.5009 DD: Two darts land randomly in the unit circle. What is the probability that they are at least 1 unit apart? Estimate = 0.413297, exact is 0.413497 DS: Expect to toss a fair die two consecutive 6's FINAL: For uniform random A and B, what is the probability that A^2/3 + B^2/3 < 1? Estimated probability = 0.293619 Exact probability = 0.294524 FLIPS: A biased coin has probability P of heads. The coin is tossed N times. What is the probability of an even number of heads? Number of tosses = 9 Probability of heads = 0.1 Probability of even number of heads = 0.567442 FLIPS: A biased coin has probability P of heads. The coin is tossed N times. What is the probability of an even number of heads? Number of tosses = 9 Probability of heads = 0.99 Probability of even number of heads = 0.08319 GALILEO: If three dice are thrown, the sum will be between 3 and 18. How many ways are there to make each sum? Total Frequency 1 0 2 0 3 1 4 3 5 6 6 10 7 15 8 21 9 25 10 27 11 27 12 25 13 21 14 15 15 10 16 6 17 3 18 1 GOLF: Probability a golf ball randomly landing in unit square is closer to center than to any edge. Estimate = 0.218978, exact is 0.218951 GR: Players A and B repeatedly play a game against each other. On each game, player A has a probability P of winning. After each game, the winner gets 1 dollar from the loser. The players begin with A nd B dollars, respectively. They play until one is bankrupt. How long will it take for one player to go bankrupt? What is the probability that A is ruined? Average number of games played is 8.92322 Probability A is ruined = 0.09968 GR: Players A and B repeatedly play a game against each other. On each game, player A has a probability P of winning. After each game, the winner gets 1 dollar from the loser. The players begin with A nd B dollars, respectively. They play until one is bankrupt. How long will it take for one player to go bankrupt? What is the probability that A is ruined? Average number of games played is 908.2 Probability A is ruined = 0.09959 GR: Players A and B repeatedly play a game against each other. On each game, player A has a probability P of winning. After each game, the winner gets 1 dollar from the loser. The players begin with A nd B dollars, respectively. They play until one is bankrupt. How long will it take for one player to go bankrupt? What is the probability that A is ruined? Average number of games played is 11.058 Probability A is ruined = 0.21197 GR: Players A and B repeatedly play a game against each other. On each game, player A has a probability P of winning. After each game, the winner gets 1 dollar from the loser. The players begin with A nd B dollars, respectively. They play until one is bankrupt. How long will it take for one player to go bankrupt? What is the probability that A is ruined? Average number of games played is 160.429 Probability A is ruined = 0.33061 INSIDE What is the probability that, choosing three points at random on the unit circle, the origin is inside the resulting triangle? Estimate = 0.249956, exact is 0.25 JB: Players A and B toss a fair die, until a 1 is rolled. On round 1, A gets 1 toss, then B gets 1 toss. On round k, A gets k tosses, then B gets k tosses. What is the probability that A wins? Estimate = 0.596862, exact is 0.596794 LIAR: Each person lies with probability 0.99 There are 41 persons Probability a true statement is transmitted as true is 0.718283 LONG: A unit stick is randomly broken in two. Then the longer piece is randomly broken again. What is the probability that the three pieces can form a triangle? Estimate = 0.386242, exact is 0.386294 MARKS: N Prob Exact 2 0.666298 0.666667 3 0.499552 0.5 4 0.400648 0.4 5 0.333651 0.333333 6 0.286223 0.285714 7 0.250123 0.25 8 0.222168 0.222222 9 0.199951 0.2 NEWTON: Estimate the probability that A: a fair die rolled 6 times will show 6 at least once; B: a fair die rolled 12 times will show 6 at least twice; C: a fair die rolled 18 times will show 6 at least 3 times. A: 0.6589 0.6651 B: 0.6251 0.6187 C: 0.5962 0.5973 OBTUSE1: Triangle has side 1 of length 1, other two side lengths chosen uniformly unit random. What are chances that the triangle is obtuse? Estimate = 0.570888, exact is 0.570796 OBTUSE2: A stick of unit length is broken into three pieces. What are chances that an obtuse triangle is formed? Estimate = 0.682335, exact is 0.682234 PLUMS: Expected distance to surface of closest of n plums in a unit spherical pudding. N Estimate Exact 5 0.0625129 0.0625 9 0.0356962 0.0357143 PP: Probability of winning pingpong, if a player has. probability P of winning a single point. P Estimate Exact 0.3 0.0263899 0.0264 0.4 0.174378 0.1744 0.5 0.5 0.5 0.6 0.825622 0.8256 RATIO1: Probability a random ratio is greater than K K Estimate Exact 2 0.499956 0.5 3 0.332646 0.333333 4 0.250311 0.25 5 0.199568 0.2 6 0.166578 0.166667 7 0.143545 0.142857 8 0.12491 0.125 9 0.110929 0.111111 RATIO2: Probability a random ratio is greater than K K Estimate 2 0.749782 3 0.555771 4 0.436749 5 0.360458 6 0.305416 7 0.265085 8 0.233752 9 0.210093 SPAGHETTI: Expected number of loops when randomly joining spaghetti ends Using 100 spaghetti strands, expected number of loops is 3.28434 Using 1000 spaghetti strands, expected number of loops is 4.43563 Using 10000 spaghetti strands, expected number of loops is 5.58693 STEVE2: Steve gets on an elevator going up. There are N higher floors. Steve wishes to go up 9 floors. There are K additional riders in the elevator, each of whom has randomly chosen one of the higher floors as destination. On average, how many times will the elevator stop until Steve reaches his floor? Estimated number of stops = 2.98903 Theoretical number is 2.98948 SQUARE_ADJ: Expected distance between random points on adjacent sides of a unit square. Exact value is 0.7652 Estimate is 0.765154 SQUARE_ANY: Expected distance between random points in a unit square. Exact value is 0.5214 Estimate is 0.521329 SQUARE_STS: Expected distance between random points on opposite sides of a unit square. Exact value is 1.0766 Estimate is 1.0767 SQUASH: What is the probability of winning at squash: P: if you serve first, Q: if you serve second. P Estimate = 0.534863, exact is 0.534863 Q Estimate = 0.465137, exact is 0.465137 TOP: Winning ratios for dreidel 2: 0.856184 0.856184 3: 0.679586 0.679586 0.679586 4: 0.524232 0.524232 0.524232 0.524232 5: 0.397955 0.397955 0.397955 0.397955 0.397955 TWINS Estimate the probability 2 twins in 20 students will be randomly assigned the same lab group of 4 students. Estimate is 0.158224, exact is 0.157895 will_you_be_alive_test Normal end of execution. 08-May-2019 15:54:35 diary off