Question
In: Statistics and Probability
Two fair coins are flipped at the same time. 1) What is the probability of getting...
Two fair coins are flipped at the same time.
1) What is the probability of getting a match (same face on both coins)? Answer for part 1 [The answer should be a number rounded to five decimal places, don't use symbols such as %]
2) What is the probability of getting at least two heads? Answer for part 2 [The answer should be a number rounded to five decimal places, don't use symbols such as %]
Solutions
Expert Solution
Thus,
Answer for part1: 0.50000
Answer for part2: 0.25000
orchestra answered 1 year agoRelated Solutions
In tossing three fair coins, what is the probability of getting at least two heads?
In tossing three fair coins, what is the probability of getting
at least two heads?
Consider an experiment where fair die is rolled and two fair coins are flipped. Define random...
Consider an experiment where fair die is rolled and two fair
coins are flipped. Define random variable X as the number shown on
the die, minus the number of heads shown by the coins. Assume that
all dice and coins are independent.
(a) Determine f(x), the probability mass function of X
(b) Determine F(x), the cumulative distribution function of X
(write it as a function and draw its plot)
(c) Compute E[X] and V[X]
A fair coin is flipped 80 times. 1) What is the probability that the first Tail...
A fair coin is flipped 80 times.
1) What is the probability that the first Tail is obtained sometime
after the 20th coin flip
(include no tails)?
2) Find an exact expression for the probability that more than 40
Heads are obtained.
3) Find an approximate value for the probability in (2) using an
appropriate Gaussian
approximation.
Problem 4) Five coins are flipped. The first four coins will land on heads with probability...
Problem 4) Five coins are flipped. The first four coins will
land on heads with probability 1/4. The fifth coin is a fair coin.
Assume that the results of the flips are independent. Let X be the
total number of heads that result.
(hint: Condition on the last flip).
a) Find P(X=2)
b) Determine E[X]
Seven fair coins are flipped. The outcomes are assumed to be independent. Let X be the...
Seven fair coins are flipped. The outcomes are assumed to be
independent. Let X be the number of heads.
What is the probability that X < 3?
What is the probability that X ≥ 4?
What is the probability that 3 ≤ X < 7
A coin is flipped seven times. What is the probability of getting heads six or fewer...
A coin is flipped seven times. What is the probability of
getting heads six or fewer times?
I know how to solve this with the probability equation.
2x2x2x2x2x2x2=128 total outcomes
Which is p1+p2=1 -> p1=1-p2-=1-1/128= 127/128 is the
answer.
But whenever I try to solve it with the permutation formula I
get a wrong answer
n!/ k!(n!-k!) = 7!/6!(7!-6!) = 7 7/128 where am I wrong? can
someone explain to me what am I doing wrong?
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with
probability 1/3 , and 1 coin that lands heads with probability 1/4
. A coin is taken from the box at random and flipped repeatedly
until it has landed heads three times. Let X be the number of times
that the coin is flipped and Y be the probability that the coin
lands heads.
(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of
Y...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with
probability 1/3 , and 1 coin that lands heads with probability 1/4
. A coin is taken from the box at random and flipped repeatedly
until it has landed heads three times. Let X be the number of times
that the coin is flipped and Y be the probability that the coin
lands heads.
(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of
Y...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with
probability 1/3 , and 1 coin that lands heads with probability 1/4
. A coin is taken from the box at random and flipped repeatedly
until it has landed heads three times. Let X be the number of times
that the coin is flipped and Y be the probability that the coin
lands heads.
(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of
Y...
Three fair coins are flipped independently. Let X be the number of heads among the three...
Three fair coins are flipped independently. Let X be the number
of heads among the three coins.
(1) Write down all possible values that X can take.
(2) Construct the probability mass function of X.
(3) What is the probability that we observe two or more heads.
(i.e., P(X ≥ 2))
(4) Compute E[X] and Var(X).
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