Suppose that you believe there is a 30% chance that the coin in your hand is...
Suppose that you believe there is a 30% chance that the coin in your hand is biased 80% in favor of heads, and a 70% chance that it’s fair. You flip it twice and get heads both times. What should you now believe is the probability that the coin is fair?
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Suppose that you believe there is a 30% chance that the coin in
your hand is...
Suppose you have two coins. One coin is fair and other is a coin with heads...
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?
Question 2 Suppose you have a fair coin (a coin is considered fair if there is...
Question 2 Suppose you have a fair coin (a coin is considered fair if there is an equal probability of being heads or tails after a flip). In other words, each coin flip i follows an independent Bernoulli distribution X Ber(1/2). Define the random variable X, as: i if coin flip i results in heads 10 if coin flip i results in tails a. Suppose you flip the coin n = 10 times. Define the number of heads you observe...
Suppose we suspect a coin is not fair we suspect that it has larger chance of...
Suppose we suspect a coin is not fair we suspect that it has larger chance of getting tails than heads, so we want to conduct a hypothesis testing to investigate this question. a:(4 pts) Let p be the chance of getting heads, write down the alternative hypothesis Ha and the null hypothesis Ho in terms of p. b: (5 pts) In order to investigate this question, we flip the coin 100 times and record the observation. Suppose we use T...
Suppose you and your roommate use a coin-flipping app to decide who has to take out...
Suppose you and your roommate use a coin-flipping app to decide who has to take out the trash: heads you take out the trash, tails your roommate does. After losing a number of flips, you start to wonder if the coin-flipping app really is totally random, or if it is biased in one direction or the other. To be fair to your roommate, you wish to test whether the app is biased in either direction, and thus a two-tailed test...
You have one fair coin and one biased coin which lands tails with probability 2/3. You...
You have one fair coin and one biased coin which lands tails with probability 2/3. You pick one of the coins at random and flip it twice. It lands trails booth times. Given this information, what is the probably that the coin that you picked is the fair one?
Suppose you flip an ordinary fair coin 60 times and amazingly it lands on heads every...
Suppose you flip an ordinary fair coin 60 times and amazingly it lands on heads every single time. What is the probability that on your next flip, it lands on tails?
Chapter 5: Discussions 1. Scheduling Employees: Suppose you own a catering company. You hire temporary employees...
Chapter 5: Discussions 1. Scheduling Employees: Suppose you own a catering company. You hire temporary employees to act as servers from the local college. Not being the most reliable employees, there is an 80% chance that any one server will actually show up for a scheduled event. For a wedding scheduled on a given Saturday you need at least 5 servers. (a) Suppose you schedule 5 employees, what is the probability that all 5 come to work? (b) Suppose you...
Suppose you have an unfair coin that is weighted so that heads comes up only 30...
Suppose you have an unfair coin that is weighted so that heads comes up only 30 percent of the time. If you flip the coin 4 times, what is the probability that you obtain at least 3 heads in the 4 flips?
Suppose you just flipped a fair coin 8 times in a row and you got heads...
Suppose you just flipped a fair coin 8 times in a row and you got heads each time! What is the probability that the next coin flip will result in a heads? Write answer as a decimal and round to 1 place after the decimal point.
3. Suppose my friend and I are tossing a biased coin (the chance of the coin...
3. Suppose my friend and I are tossing a biased coin (the chance of the coin landing heads is 0.48). I get one dollar each time the coin lands heads, and I have to pay one dollar to my friend each time it lands tails. I will stop playing if my net gain is three dollars. (a)What is the chance that I will stop after exactly three tosses? (b) What is the chance that I will stop after exactly four...
Question 2 Suppose you have a fair coin (a coin is considered fair if there is an equal probability of being heads or tails after a flip). In other words, each coin flip i follows an independent Bernoulli distribution X Ber(1/2). Define the random variable X, as: i if coin flip i results in heads 10 if coin flip i results in tails a. Suppose you flip the coin n = 10 times. Define the number of heads you observe...
Suppose we suspect a coin is not fair we suspect that it has larger chance of getting tails than heads, so we want to conduct a hypothesis testing to investigate this question. a:(4 pts) Let p be the chance of getting heads, write down the alternative hypothesis Ha and the null hypothesis Ho in terms of p. b: (5 pts) In order to investigate this question, we flip the coin 100 times and record the observation. Suppose we use T...
Chapter 5: Discussions 1. Scheduling Employees: Suppose you own a catering company. You hire temporary employees to act as servers from the local college. Not being the most reliable employees, there is an 80% chance that any one server will actually show up for a scheduled event. For a wedding scheduled on a given Saturday you need at least 5 servers. (a) Suppose you schedule 5 employees, what is the probability that all 5 come to work? (b) Suppose you...
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