Question

-Determine the probability of the following events. State any assumptions that you use.

1.) What is the probability of not tossing 3 heads with three fair coins?

- Odds. Use the definition given in the text to find both the odds for and the odds against the following events.

1.) Flipping two fair coins and getting 2 heads

- Use the definition of odds in betting to find the following odds.

1.) The odds on (against) your bet are 6 to 5. If you bet $20 and win, how much will you gain.

Answer #1

Find the probability of each of the following events:
(i) Tossing a coin 5 times with the outcome of five heads.
(ii) Tossing four coins with the outcome of two heads and two
tails in any order.

You are given 3 to 2 odds against tossing three heads with
three? coins, meaning you win ?$3 if you succeed and you lose ?$2
if you fail. Find the expected value? (to you) of the game. Would
you expect to win or lose money in 1? game? In 100? games?
Explain.

A selection of coin is known to be either fair (with a
probability 0.5 of coming up heads or tails when flipped) or biased
(with a probability 0.75 of tails, 0.25 of heads.) Further. it is
known that 1/10 of the coins are biased. a) You select a coin at
random. What are the prior odds (not probability) that you have
picked a biased coin? b) You select a coin at random and flip it;
you get tails. What are...

$ (prize)
$(profit)
x = # of
heads
P(x)
$1
$3
0
0.03125
$ 1
$3
1
0.15625
$1
$ 1
2
0.31250
$1
$1
3
0.31250
$ 1
$0
4
0.15625
$ 1
$0
5
0.03125
1. A fair coin is tossed five times. The probability of
observing “x” heads among the 5 coins is given in the table above.
A particular game consists of tossing a fair coin 5 times. It costs
$1 to play the game; you...

Consider two coins, one fair and one unfair. The probability of
getting heads on a given flip of the unfair coin is 0.10. You are
given one of these coins and will gather information about your
coin by flipping it. Based on your flip results, you will infer
which of the coins you were given. At the end of the question,
which coin you were given will be revealed.
When you flip your coin, your result is based on a...

2. Probability
For the following events:
a) State whether these are and or or probabilities
b) State whether they are independent or dependent (for and ) or
overlapping or
non-overlapping (for or )
c) Find the probability of the event.
Randomly selecting a committee of seven from a pool of 15 men and
15 women, and ending up
with all women.
Getting a sum of either 6 or 8 on a roll of two dice.
Getting at least one parking...

1) Four fair coins are tossed. Find the following
probabilities:
a) P(getting 2 heads and 2 tails)
b) P(getting at least one heads)
c) P(getting 2 heads given there is at least one heads)
2. The probability that a new Duracell battery is defective is
1%. Suppose that Janet buys a 100 pack of batteries from Costco.
Find the following probabilities:
a) P(3 batteries are defective)
b) P(none of the batteries are defective)

Suppose you roll, two
6-sided dice Write any probability as a decimal to three place
values and the odds using a colon. Determine the following:
1. The probability
that you roll a sum of seven (7)
2. The odds for
rolling a sum of four (4) is
3. The odds against
the numbers on both dice being the same is
Suppose you have a bag
with the following marbles: four (4) red, six (6) pink, two (2)
green, and seven...

You have a coin that you suspect is not fair (i.e., the
probability of tossing a head (PH) is not equal to the probability
of tossing a tail (PT) or stated in another way: PH ≠ 0.5). To
test yoursuspicion, you record the results of 25 tosses of the
coin. The 25 tosses result in 17 heads and 8 tails.
a) Use the results of the 25 tosses in SPSS to construct a 98%
confidence interval around the probability of...

7. If you flip 10 fair coins, what is the probability that: (a)
Exactly 5 of them are “heads”? (b) At
least 8 of them are “heads”?
8. Urn A has four red balls and two white balls, and urn B has
three red balls and four white
balls. A fair coin is tossed. If it lands heads up, a ball is
drawn from urn A; otherwise, a ball is
drawn from urn B. Compute (a) the probability a red...

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