Suppose we toss a weighted coin, for which the probability of getting a head (H) is...
Suppose that the probability of getting a head on the ith toss of an ever-changing coin is f(i). How would you efficiently compute the probability of getting exactly k heads in n tosses?
A coin is weighted so that the probability of obtaining a head in a single toss is 0.6. If the coin is tossed 25 times, find the following probabilities. (Round your answers to fou decimal places.) (a) fewer than 12 heads 0.0778 (b) between 12 and 15 heads, inclusive 4970 X (c) more than 19 heads You may need to use the appropriate table in the Appendix of Tables to answer this question Need Help? med 16. (-/3 Points DETAILS...
The probability of getting heads from throwing a fair coin is 1/2 The fair coin is tossed 4 times. What is the probability that exactly 3 heads occur? 1/4 The fair coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first outcome was a head? 3/8 The fair coin is tossed 4 times. What is the probability that exactly 3 heads occur given that the first outcome was a tail? 1/8 The...
1. There is this coin that is not balanced. The probability of getting a head is four times the probability of getting a tail. Suppose this coin is tossed 5 times. Give the probability of getting at least 1 head. Express your answer as a decimal to several places past the decimal or as a common fraction. Show work.
2. A coin is altered so that the p coin is flipped three times as altered so that the probability of getting a head on every flip is 0.6. Suppose this (*) is flipping the coin a binomial experiment? Explain by checking if the four properties of binomial experiments are satisfied. (b) What is the probability that there are at least two heads? (c) What is the probability that an odd number of heads turn out in 3 flips? (d)...
9.74. Suppose we toss a biased coin independently until we get two heads or two tails in total. The coin produces a head with probability p on any toss. 1. What is the sample space of this experiment? 2. What is the probability function? 3. What is the probability that the experiment stops with two heads?
Suppose we toss a coin (with P(H) p and P(T) 1-p-q) infinitely many times. Let Yi be the waiting time for the first head so (i-n)- (the first head occurs on the n-th toss) and Xn be the number of heads after n-tosses so (X·= k)-(there are k heads after n tosses of the coin). (a) Compute the P(Y> n) (b) Prove using the formula P(AnB) P(B) (c) What is the physical meaning of the formula you just proved? Suppose...
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...
A biased coin with probability 0.6 to land on head is flipped 6 times, calculate the probability of: - exactly two heads, - at most one tail, - even number of heads.
An experiment consists of tossing an unfair coin (53% chance of landing on heads) a specified number of times and recording the outcomes. (a) What is the probability that the first head will occur on the second trial? (Use 4 decimal places.) Does this probability change if we toss the coin three times? What if we toss the coin four times? The probability changes if we toss the coin three times, but does not change if we toss the coin...