Question
In: Statistics and Probability
You are presented with 400 coins. 250 of them are fair coins, while the remaining 150...
You are presented with 400 coins. 250 of them are fair coins, while the remaining 150 land heads with probability 0.60. Part a: If you select 50 of the coins at random, what is the probability that less than half of them are fair coins? Part b: What is the probability that a randomly selected coin flipped once will land heads? Part c: Consider the following procedure: 1. Select one of the coins randomly. 2. Flip the coin. 3. Record whether the coin lands tails. 4. Replace the coin and throroughly mix the coins. If this procedure is repeated 100 times, what is the probability that the number of times that the coin lands tails will be less than 30?
Solutions
orchestra answered 1 year agoRelated Solutions
You are presented with 400 coins. 250 of them are fair coins, while the remaining 150...
You are presented with 400 coins. 250 of them are fair coins,
while the remaining 150 land heads with probability 0.65.
Part a: If you select 60 of the coins at random, what is the
probability that less than half of them are fair coins?
Part b: What is the probability that a randomly selected coin
flipped once will land heads?
Part c: Consider the following procedure:
1. Select one of the coins randomly.
2. Flip the coin.
3. Record...
You are presented with 400 coins. 250 of them are fair coins, while the remaining 150...
You are presented with 400 coins. 250 of them are fair coins,
while the remaining 150 land tails with probability 0.60.
Part a: If you select 60 of the coins at random, what is the
probability that less than half of them are fair coins?
Part b: What is the probability that a randomly selected coin
flipped once will land tails?
Part c: Consider the following procedure:
1. Select one of the coins randomly.
2. Flip the coin.
3. Record...
Suppose you have a bag of 100 coins. Ninety of them are fair coins, which is...
Suppose you have a bag of 100 coins. Ninety of them are fair
coins, which is P(H) = P(T) = 1/2. The other 10 coins are biased ,
they have tail (T) on both sides. Let X = {X1, X2, · · · , X100} be
a random variable denoting the the total number of heads in the 100
coin flips.
a. How many possible values X can take? For example, if one
tosses two fair coins, the number of...
You have 100 coins, and 99 of them are fair (equal probability of heads or tails)....
You have 100 coins, and 99 of them are fair (equal probability
of heads or tails). One of them is weighted and has a 90%
probability of landing on heads. You randomly choose one of the 100
coins. Find the probability that it is a weighted coin, under the
following scenarios: (Hint: if your calculator can’t compute 100!,
R can, just type factorial(100))
(a) You flip it 10 times and lands on heads 10 times (b) You
flip it 10...
You have two coins, one of which you know to be fair and the other of...
You have two coins, one of which you know to be fair and the
other of which has a probability of turning up heads of 0.7, but
you can’t tell which one is which. You choose one coin at random
and flip it ten times getting an equal number of heads and tails.
What is the probability that you chose the unfair coin?
You have 3 coins that look identical, but one is not a fair coin. The probability...
You have 3 coins that look identical, but one is not a fair
coin. The probability the unfair coin show heads when tossed is
3/4, the other two coins are fair and have probability 1/2 of
showing heads when tossed.
You pick one of three coins uniformly at random and toss it n
times, (where n is an arbitrary fixed positive integer).
Let Y be the number of times the coin shows heads. Let X be the
probability the coin...
Consider the following game. You are to toss three fair coins. If three heads or three...
Consider the following game. You are to toss three fair coins.
If three heads or three tails turn up, your friend pays you $20. If
either one or two heads turn up, you must pay your friend $5. What
are your expected winnings or losses per game?
Assume we are flipping 1000 fair coins. What can you say about the probability that you...
Assume we are flipping 1000 fair coins. What can you say about
the probability that you will get at least 3/5 of them to be heads?
Compare the 3 bounds (Markov, Chebyshev, Chernoff), and try
plugging in some leargevalue of n to see how muchs
they differ!
If you toss five fair coins, in how many ways can you obtain at least one...
If you toss five fair coins, in how many ways can you obtain at
least one tail?
The local county fair this summer has a challenge with a winning prize of $250. You...
The local county fair this summer has a challenge with a winning
prize of $250. You have to throw a spear at an underwater target
that is sitting 1 meter below the water’s surface in a water
trough. The challenge is arranged such that you have to stand on a
platform that places your eyes 3 m above the bottom of the
trough (and therefore 3 vertical meters above the target). From
your location, you see the target 30° below...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Microcomputers and handheld calculators – An argument can be made that the development of powerful, inexpensive...
- . Explain the following terms: a. Purpose of an audit b. Accounting cycl
- I'm trying to make this C++ loan calculator but I can't get the program to output...
- Evaluate the principles of systems thinking and the role of systems thinking in organisational change.
- List 5 processes in your current company that would be impacted by a power outage. Rank...
- You would like to buy a house that costs $350,000. You have $50,000 in cash that...
- Etonic Inc. is considering an investment of $375,000 in an asset with an economic life of...
ADVERTISEMENT