Question

Toss a fair coin five times and record the results. Use T to denote tails facing up and H to denote heads facing up.

(a) [5 points] How many different results can we get?

(b) [10 points] What is the probability that there is
**only one T** in the result? Round answer to 4
decimal .

(c) [10 points] What is the probability that **at least
two T's** in the result? Round answer to 4 decimal .

Answer #1

You toss a fair coin four times. The probability of two heads
and two tails is

(a) A fair coin is tossed five times. Let E be the event that an
odd number of tails occurs, and let F be the event that the first
toss is tails. Are E and F independent?
(b) A fair coin is tossed twice. Let E be the event that the
first toss is heads, let F be the event that the second toss is
tails, and let G be the event that the tosses result in exactly one
heads...

You toss a fair coin six times. What is the probability that at
least one toss results in a tail appearing? Round your answer to
four decimal places.

Toss a fair coin for three times and let X be the number of
heads.
(a) (4 points) Write down the pmf of X. (hint: first list all
the possible values that X can take, then calculate the probability
for X taking each value.)
(b) (4 points) Write down the cdf of X.
(c) (2 points) What is the probability that at least 2 heads
show up?

Let H (Heads) and T (Tails) denote the two outcomes of a random
experiment of tossing a fair coin. Suppose I toss the coin infinite
many times and divide the outcomes (which are infinite sequences of
Heads and Tails) into two types of events:
(a) the portion of H or T of is exactly one half
(e.g.HTHTHTHT... or HHTTHHTT...)
(b) the portion of H or T is not one half (i.e. the complement
of event (a). e.g. HTTHTTHTT...). What are...

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 three times. Which of the following
events are independent? Give mathematical justification for your
answer.
A=
{“heads on first toss”}; B=
{“an odd number of heads”}.
A=
{“no tails in the first two tosses”}; B=
{“no heads in the second and third
toss”}.

Toss the coin four times. If the coin lands either all heads or
all tails, reject H0: p=1/2. (The p denotes the chance for the coin
to land on heads.) Complete parts a and b.
(a) What is the probability of a Type I error for this
procedure?
(b) If p = 4/5, what is the probability of a Type II error for
this procedure?

Toss an unfair coin with probability of tails as 0.4 for 15
times. What is the probability that tails shows up more than 2
times but less than 6 times?
Group of answer choices
0.398
0.624
0.605
0.376

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