Question
In: Math
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]
Solutions
milcah answered 7 months agoRelated Solutions
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...
If a heads is flipped, then the coin is flipped 4 more times and the number...
If a heads is flipped, then the coin is flipped 4 more times and
the number of heads flipped is noted; otherwise (i.e., a tails is
flipped on the initial flip), then the coin is flipped 3 more times
and the result of each flip (i.e., heads or tails) is noted
successively. How many possible outcomes are in the sample space of
this experiment?
For the following exercises, four coins are tossed. Find the probability of tossing either two heads or three heads.
For the following exercises, four coins are tossed.Find the probability of tossing either two heads or three heads.
There are 3 coins which when flipped come up heads, respectively, with probabilities 1/4, 1/2, 3/4....
There are 3 coins which when flipped come up heads,
respectively, with probabilities 1/4, 1/2, 3/4. One of these coins
is randomly chosen and continually flipped.
(a) Find the expected number of flips until the first head.
(b) Find the mean number of heads in the first 8 flips.
a) A coin is flipped 6 times, find the probability of getting exactly 4 heads. Hint: The Binomial...
a) A coin is flipped 6 times, find the probability of
getting exactly 4 heads. Hint: The Binomial Distribution
Table can be very helpful on questions 19-21. If
you use the table for this question, give your answer exactly as it
appears. If you calculated your answer, round to the
thousandths place.
b) A coin is flipped 6 times. Find the probability of getting at
least 3 heads. If you used a table to help find your answer, give
it to the thousandths place....
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).
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 %]
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?
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