Question

(a) Use the central limit theorem to determine the probability that if you toss a coin 50 times, you get fewer than 20 heads.

(b) A coin is continuously tossed until the heads come up 20th time. Use the central limit theorem to estimate the probability that more than 50 coin tosses are required to get the 20th head.

(c) Compare your answers from parts (a) and (b). Why are they close but not exactly equal?

Answer #1

Use the DeMoivre-Laplace limit theorem to approximate the
probability of getting heads exactly 50 times in 100 tosses of a
fair coin.

You toss a coin 192 times. Find the probability that exactly 96
of the 192 tosses will be heads.

A biased coin is tossed repeatedly. The probability of getting
head in any particular toss is 0.3.Assuming that the tosses are
independent, find the probability that 3rd head appears exactly at
the 10th toss.

A fair coin is tossed three times. What is the probability
that:
a. We get at least 1 tail
b. The second toss is a tail
c. We get no tails.
d. We get exactly one head.
e. You get more tails than heads.

Suppose you toss a coin 100 times. Should you expect to get exactly
50 heads? Why or why not?
A. Yes, because the number of tosses is even, so if the coin
is fair, half of the results should be heads.
B. No, because the chance of heads or tails is the same, the
chance of any number of heads is the same.
C. No, there will be small deviations by chance, but if the
coin is fair, the result...

Suppose you toss a fair coin 10,000 times. Should you expect to
get exactly 5000 heads? Why or why not? What does the law of
large numbers tell you about the results you are likely to get?
Choose the correct answer below.
1)Should you expect to get exactly 5000 heads? Why or why
not?
A)You shouldn't expect to get exactly 5000 heads, because you
cannot predict precisely how many heads will occur.
B.You shouldn't expect to get exactly 5000 heads,...

A special weighted coin is found to land on heads 52% of the
time. This coin is flipped 100 times. Use Central Limit Theorem and
round answer to the nearest 10th. What is the probability that
Heads will appear more than 59 out of these 100 tosses? Round to
the nearest 10th of a percent.

(Q6) A coin is biased so that the probability of tossing a head
is 0.45. If this coin is tossed 55 times, determine the
probabilities of the following events. (Round your answers to four
decimal places.)
(a) The coin lands heads more than 21 times.
(b) The coin lands heads fewer than 28 times.
(c) The coin lands heads at least 20 times but at most 27
times.
(Q7) A company finds that one out of three employees will be...

Suppose you toss an unfair coin 8 times independently. The
probability of getting heads is 0.3. Denote the outcome to be 1 if
you get heads and 0 if you get tails.
1.Write down the sample space.
2. What is the probability of the event that you get a head or a
tail at least once?
3. If you get 8 same toss you will get x dollars, otherwise you
will lose one dollar. On average, how large should x...

You have a coin that has a probability p of coming up Heads.
(Note that this may not be a fair coin, and p may be different from
1/2.) Suppose you toss this coin repeatedly until you observe 1
Head. What is the expected number of times you have to toss it?

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