Question

4. We have 10 coins, which are weighted so that when flipped the kth coin shows heads with probability p = k/10 (k = 1, . . . , 10).

(a) If we randomly select a coin, flip it, and get heads, what is the probability that it is the 3rd coin? Answer: 3/55 '

(b) What is the probability that it is the kth coin? Answer: k/55

(c) If we pick two coins and they both show heads, what is the probability that one of them is the 5th coin? So far, for part (c), I have P(E5 | HH) = (1/18)/P(HH), but I am not confident in how to find P(HH).

Answer #1

Thirty biased coins are flipped once. The coins are weighted so
that the probability of a head with any coin is 0.40. What is the
probability of getting at least 16 heads?
The answer is 0.0681. How do I solve this??

There are two coins and one of them will be chosen randomly and
flipped 10 times. When coin 1 is flipped, the probability that it
will land on heads is 0.50. When coin 2 is flipped, the probability
that it will land on heads is 0.75. What is the probability that
the coin lands on tails on exactly 4 of the 10 flips? Round
the answer to four decimal places.

I have a fair coin and a weighted coin that lands heads 60% of
the time. I grab a coin at random. I flip that coin 5 times and get
heads 4 times and tails once.
What is the probability that the coin I grabbed was the weighted
coin? (answer to 3 decimal places)

Suppose I have two biased coins: coin #1, which lands heads with
probability 0.9999, and coin #2, which lands heads with probability
0.1. I conduct an experiment as follows. First I toss a fair coin
to decide which biased coin I pick (say, if it lands heads, I pick
coin #1, and otherwise I pick coin #2) and then I toss the biased
coin twice. Let A be the event that the biased coin #1 is chosen,
B1 the event...

If I tell you that I have a coin, but it is a special coin. In
that, I mean that it is not a 50/50 coin. However, I don't know how
likely it is for it to land on heads (or tails). So we decide to
flip it 10 times and we get 40% heads (which is 0.40 as a
proportion). Are you willing to say that it is a 40/60 coin? Why or
why not?
after we flipped it...

3. A fair coin is flipped 4 times.
(a) What is the probability that the third flip is tails?
(b) What is the probability that we never get the same outcome
(heads or tails) twice in a row?
(c) What is the probability of tails appearing on at most one of
the four flips?
(d) What is the probability of tails appearing on either the
first or the last flip (or both)?
(e) What is the probability of tails appearing...

Q1. I have two coins in my pocket, one is a fair coin,
the other has heads on both sides. I pick one at random, and
without looking at what it is, I toss it four times. I get four
heads. (HHHH).
(I) What is the probability that I picked the fair
coin?
(II) What is your answer if I got N heads in a row
rather than four?
Q2. A, B are cowboys. A hits every shot. A has...

4. The Casino Control Commission takes a coin from a casino it
suspects to be unfair. They flip the coin 10 times and lands on
heads 8 times.
(a) What is the probability that a fair coin would land on heads
at least 8 times?
(b) Based on your answer to the last question, do you think the
coin is unfair? Explain.
5. Every day, Janet either takes the bus or drives her car to
work. She drives her car...

You will flip two coins together 10 times. You are interested in
the outcome where both coins land on heads. Let X be the number of
times you observe this outcome. Answer Question 1 through 4.
1. What are the possible values for x? (values the random
variable X can take)
2. Is X binomial random variable? If so, state its parameter n
and p. If not, explain why.
3. Find the probability that you will see both coins landing...

SCENARIO : OPIOID WITHDRAWL
OUTGOING NURSE : So we have an Evet Ogam. She is a 34-year-old
female brought in by ambulance, last night at 1800 for a heroin
overdose.
She was given 2 doses of naloxone, 2mg each dose. She vomited
twice following the naloxone. Following stabilization in the ER,
she has been brought up to our floor for monitoring.
Pt is allergic to aspirin and has a history of back surgery in
2012,
Pt has been admitted twice...

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