Suppose that Anna and Ben will each toss a fair coin until an outcome of Heads is obtained. (I.e., each person will toss their coin until they obtain an outcome of Heads.) What is the probability that it will take Ben MORE THAN TWICE as many tosses as it takes Anna? (Make the usual assumptions regarding tosses of fair coins.)
Suppose that Anna and Ben will each toss a fair coin until an outcome of Heads...
Q3. Suppose we toss a coin until we see a heads, and let X be the number of tosses. Recall that this is what we called the geometric distribution. Assume that it is a fair coin (equal probability of heads and tails). What is the p.m.f. of X? (I.e., for an integer i, what is P(X=i)? What is ?[X]? ({} this is a discrete variable that takes infinitely many values.)
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.
Suppose you toss a fair coin until you’ve gotten a total of 2 heads or a total of 4 tails (neither the 2 heads nor the 4 tails occur necessarily consecutively), and then you stop. What is the probability that your last coin toss came up tails?
Suppose that I toss a fair coin 100 times. Write 'p-hat' for the proportion of Heads in the 100 tosses. What is the approximate probability that p-hat is greater than 0.6? 0.460 0.023 0.540 We can't do the problem because we don't know the probability that the coin lands Heads uppermost 0.977
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,...
On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is 0.5. If you toss a coin twice and get heads on the first toss, are you guaranteed to get tails on the second toss? Explain.Explain why – 0.41 cannot be the probability of some event.Explain why 1.21 cannot be the probability of some event.Explain why 120% cannot be the probability of some event.Can the number 0.56 be the probability of...
You toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair, i.e., the probability of heads is 1/2 and the probability of tails is y. This means every occurrence of a head must be balanced by a tail in one of the next two or three tosses. if I flip the coin many, many times, the proportion of heads will be approximately %, and this proportion will tend to get closer and...
Suppose you flip a fair coin repeatedly until you see a Heads followed by another Heads or a Tails followed by another Tails (i.e. until you see the pattern HH or TT). (a)What is the expected number of flips you need to make? (b)Suppose you repeat the above with a weighted coin that has probability of landing Heads equal to p.Show that the expected number of flips you need is 2+p(1−p)/1−p(1−p)
Amanda, Becca, and Charise toss a coin in sequence until one person “wins” by tossing the first head. a) If the coin is fair, find the probability that Amanda wins. b) If the coin is fair, find the probability that Becca wins. c) If the coin is fair, find the probability that Charise wins. d) The coin is no longer fair. The probability that the coin comes up heads on an individual toss is p, for 0<p<1. Plot each players...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was found to be 0.58. However, the margin of error for the estimate on the proportion of heads in all tosses was too big. Suppose you want an estimate that is in error by no more than 0.05 at the 95% confidence level. (a) What is the minimum number of tosses required to obtain this type of accuracy? Use the prior sample proportion in your...