Amrita flips a biased coin repeatedly until she observes that both a head and a tail appear. The probability that a head will appear on a single flip is p, for 0 < p < 1. Find the probability mass function of N, the number of flips required to observe both a head and a tail. Hint: If N is the flip number that ends the experiment then that means that the N − 1 flips previous to flip N must all be the same as each other but different from the Nth flip. Also think about what the smallest value in the support of N must be. Finally remember that there are two cases: a sequence of tails followed by a head, or a sequence of head’s followed by a tail.

Amrita flips a biased coin repeatedly until she observes that both a head and a tail appear. The probability that a head will appear on a single flip is p, for 0 < p < 1. Find the probability mass function of N, the number of flips required to observe both a head and a tail. Hint: If N is the flip number that ends the experiment then that means that the N − 1 flips previous to flip N must all be the same as each other but different from the Nth flip. Also think about what the smallest value in the support of N must be. Finally remember that there are two cases: a sequence of tails followed by a head, or a sequence of head’s followed by a tail.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Urn A contains five white balls and three black balls. Urn B contains seven white balls and four black balls. A ball is drawn from Urn A and then transferred to Urn B. A ball is then drawn from Urn B. What is the probability that the transferred ball was black given that the second ball drawn was black? (Round your answer to three decimal places.)
A sample of 51observations will be taken from an infinite population. The population proportion equals 0.85. The probability that the sample proportion will be between 0.9115 and 0.946 is a. 0.0345 O b. 0.8633 O c. 0.0819 d. 0.6900 NEXT PAGE AGE
The reported rate for colorblindness for men ages 65 and older is 12%. Assume this estimate is the true population proportion of men ages 65 and older. A SRS of 25 men ages 65 and older is taken. Calculate the probability that proportion of men ages 65 and older who have colorblindness is more than 0.10. A. 3783 B. 6217 C. This can’t be done because np is not greater than D. This can’t be done because n is not greater than 30 and we are not told that the variable is normally distributed.
An otherwise fair six-sided die has been tampered with in an attempt to cheat at a dice game. The effect is that the 1 and 6 faces have a different probability of occurring than the 2, 3, 4 and 5 faces. Let 0 be the probability of obtaining a 1 on this biased die. Then the outcomes of rolling the biased die have the following probability mass function. Table 1 The p.m.f. of outcomes of rolls of a biased die Outcome 3 6. Probability 0 1(1– 20) |(1- 20) ļ0– 20) |(1– 20) 0 Studies of the size and range of wild animal populations often involve tagging observed individual animals and recording how many times each is caught in a trap (from which it is then released back into the wild). The dataset presented in Table 3 consists of the numbers of times cach of n= 331 wood mice were caught in a particular trap (over a two-year time period). Table 3 Numbers of trappings of wood mice Times trapped Frequency 3 4 20 9. 71 59 41 39 26 19 12 9. Times trapped 10 Frequency 11 12 13 14 15 16 17 18 8 4 9…
A fair six-sided die is rolled independently 900 times. Find the lower bound for the probability of getting 120 to 180 sixes? A. 1/6 B. 1/15 C. 31/36 D. 2/15 E. 1/5
An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 40% of all those making reservations do not appear for the trip. Suppose the probability distribution of the number of reservations made is given in the accompanying table (Figure 1) What is the probability mass function of X= 1,2,3,4
A purchaser of electric relays buys from two suppliers, A and B. Supplier A supplies two of every three relays used by the company. If 90 relays are selected at random from those in use by the company, find the probability that at most 59 of these relays come from supplier A. Assume that the company uses a large number of relays. (Use the normal approximation. Round your answer to four decimal places.)
Suppose the numbers 1, 2, 3, and 6 are written on cards. Which are placed in a box. Two cards are picked from the box. Let X be the random variable that gives the products of the two numbers drawn. a. Construct the probability mass function of X b. Construct the histogram for the pmf c. What is P(X=6)? d. What is P(X ≤ 10)?
Cody and Sierraagree to meet at the fitness center for a morning workout. They agree to meet sometime between 6:00am and 7:00am. They have an agreement that if either of them has to wait more than 15minutes for the other one, the workout is canceled. What is the probability that they will work out ? Assume that Cody and Sierra’s arrival times are independent and uniformly distributed between 6:00am and 7:00am.
For each probability, the first column is for the TI command with no spaces, and the second column is for the probability rounded to three decimal places.Suppose a random variable, x, arises from a binomial experiment. If n = 22, and p = 0.85, find: TI Command Probability a. P(x = 18) = b. P(x ≤ 3) = c. P(x ≥ 20) =
According to recent reports, currently 39% of the population of NC (adults and children) has been fully vaccinated against Covid. Suppose of random sample of 400 individuals from the population of NC is selected. Let x represent the number in the sample who are fully vaccinated. a. State the values of n and p for this binomial experiment. b. Find the probability that exactly 156 in the sample have been fully vaccinated. Round to 4 decimal places.
A life insurance salesman sells on the average 3 life insurance policies per week. Use Poisson's law to calculate the probability that in a given week he will sell some policies 0.95021 0.61611 None of the choices O 0.32929