Question
In: Math
Please double-check, provide work, and show explanation Assume I toss a fair coin exactly 17 times....
Please double-check, provide work, and show explanation
Assume I toss a fair coin exactly 17 times. Find the probability of the following outcomes:
A) 4 tails
B) 17 tails
C) 5 heads
D) 17 heads
E) 13 or more tails
F) 5 or fewer tails
Solutions
milcah answered 3 weeks agoRelated Solutions
If I toss a fair coin 50,000 times which of the following is true? a) the...
If I toss a fair coin 50,000 times which of the following is
true?
a) the number of heads should be between 15,000 and 25,000.
b) the proportion of heads should be close to 50%.
c) the proportion of heads in these tosses is a parameter.
d) the number of heads should be exactly 25,000.
e) the proportion of heads will be close to 1.
I toss a fair coin 20 times. (a) Calculate the probability of tossing 18 or more...
I toss a fair coin 20 times.
(a) Calculate the probability of tossing 18 or more heads
exactly.
(b) Now perform the same calculation, approximating the actual
binomial distribution with a normal distribution, picking a proper
random variable, and using the correct mean and variance. (c) Do
the results reasonably agree?
Suppose you toss a fair coin 4 times. Denote the outcome to be 1 if you...
Suppose you toss a fair coin 4 times. Denote the outcome to be 1
if you get a head and 0 if a tail.
a) Write down the sample space Ω
b) What is the probability of the event that you get head at
least once?
c) If you get four same toss you will get 10 dollars, otherwise
you will lose 2 dollars. On average, will you win or lose?
Suppose you toss a fair coin 10 times resulting in a sequence of heads (H) and...
Suppose you toss a fair coin 10 times resulting in a sequence of
heads (H) and tails (T). Let X be the number of times that the
sequence HT appears. For example, HT appears thrice in
THTHHTHHHT Find E(X).
Use Indicator random variables.
What are the probabilities that... 1) You toss a fair coin 6 times and you get...
What are the probabilities that...
1) You toss a fair coin 6 times and you get exactly 4 heads?
2) You toss a fair coin 6 times and you get at least two
heads?
Suppose you toss a fair coin 10 times resulting in a sequence of heads (H) and...
Suppose you toss a fair coin 10 times resulting in a sequence of
heads (H) and tails (T). Let X be the number of times that the
sequence HT appears. For example, HT appears thrice in
THTHHTHHHT
Find E(X). Hint: Use Indicator random variables.
Suppose you toss a fair coin 10 times. (a) Calculate the probability of getting at least...
Suppose you toss a fair coin 10 times.
(a) Calculate the probability of getting at least 6 heads, using
the exact distribution.
(b) Now repeat the calculate above, but approximate the
probability using a normal random variable. Do your calculation
both with and without the histogram correction. Which one is closer
to the true answer?
Now suppose you toss a fair coin 1000 times.
(c) What is the probability of getting at least 520 heads? You
can approximate this using...
Both Alice and Bob toss a fair coin three times. The probability that Alice records a...
Both Alice and Bob toss a fair coin three times. The probability
that Alice records a different numbers of heads than Bob is given
by A/B, where A and B are relatively prime integers (greatest
common divisor is 1). Find A + B.
Flip a coin 30 times and document the result of each toss. Then provide both the...
Flip a coin 30 times and document the result of each toss. Then
provide both the empirical and theoretical probability
distributions. Use the appropriate expression for probability.
We model the experiment where we toss a fair coin 4 times as follows. The sample...
We model the experiment where we toss a fair coin 4 times as
follows. The sample space Ω is the space of (ordered) binary
vectors of length 4. A 1 in the i-th position of such a binary
vector indicates Heads at the i-th toss. The probability measure
(P) on Ω is defined as P(A)=|A| / |Ω| for all A⊂Ω. Let Ai be the
event that the ith toss is Heads, i = 1,...,4. (a) Give all
outcomes in A3....
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