Question

Two coins are tossed. If two heads are thrown, letters are
chosen from the word TWOFOLD. If one head is thrown, letters are
chosen from the word ONEROUS. If no heads are thrown, letters are
chosen from the word NOMAD. Whichever word is used, we draw letters
one at a time, the drawing to be **without
replacement.** until a vowel is obtained. What is the
expected number of letters then drawn?

Answer #1

Two coins are tossed. If two heads are thrown, letters are
chosen from the word TWOFOLD. If one head is thrown, letters are
chosen from the word ONEROUS. If no heads are thrown, letters are
chosen from the word NOMAD. Whichever word is used, we draw letters
one at a time, without replacement, until a vowel is obtained. What
is the expected number of letters then drawn?
Answer is 59/30. Please show each steps clearly and
specifically. Thank you.

Choose letters, one at a time and at random, notably
without replacement, from the word
STATISTICS, until precisely two T’s have been
drawn. Let X = the number of letters chosen.
Find the following:
Part A: E(X)
Part B: Var(X)

1.
two coins are tossed, find the probability that two heads are
obtained. note: each coin has two possible outcomes H (heads) and T
(tails).
2. which of these numbers cannot be a probability? why?
a) -0.00001
b) 0.5
c) 20%
d)0
e) 1
3. in a deck of 52 cards, what is the probability of drawing a
three of spades, and then a four of clubs, without
replacement?
4. what is the probability of the same outcome in #3,...

Part 1. Two fair coins are tossed and we are told that one
turned up “Heads”. What is the probability that the other turned up
“Tails”?
Part 2. Two fair coins are tossed, and we get to see only one,
which happened to turn up “Heads”. What is the probability that the
hidden coin turned up “Tails”?
*Remark This problem is really different from the previous
one!

a) How many four-letter words can be formed from the letters of
the word TAUDRY if each letter can only be used one time in a word?
Y is NOT considered a vowel in this word.
b) How many contain the letter Y?
c) How many contain all the vowels?
d) How many contain exactly three consonants?
e) How many of them begin and end in a consonant?
f) How. many begin with a D and end in a vowel...

a) How many four-letter words can be formed from the letters of
the word TAUDRY if each letter can only be used one time in a word?
Y is NOT considered a vowel in this word.
b) How many contain all the vowels?
c) How many contain exactly three consonants?
d) How many of them begin and end in a consonant?
e) How many contain both D and Y?

From a standard deck of cards two cards are chosen without
replacement one at a time. Find the probability of drawing a face
card given that the first card was red.(EXPLAIN)

k numbers are chosen at random from the set {1,2,...,N}, one
after the other, without replacement. Find the probabilities of
each of these events:
1. The set of numbers drawn is {1,2,...,k}. (Note that they need
not be drawn in that exact order since we only care about the
set.)
2. The numbers are chosen in an ascending order.
3. How do your answers to parts 1 and 2 change if the numbers
are drawn one after the other, but...

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...

We are drawing two cards without replacement from a standard
52-card deck. Find the probability that we draw at least one
red card.
The probability is
nothing.

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