Question

1)From a deck of 52 cards two cards are drawn Without replacement. What is the probability that both cards are Queens?

2) From set of 12 books how many combinations are there of 12 books taken 4 at a time?

3) A club has 15 members. They must elect a Chairperson, a president, a treasure and a secretary

4) How many different permutations represent the number of possible sets of officers?

5) Given the set of random variables and their associated probabilities, This is a Probability Distribution because the probabilities add up to 1

X P(x)

0 1/16

4/16

6/16

4/16

1/16

∑P(x) = 16/16 =1 Find the Mean μ of this probability distribution and standard deviation ð of the distribution.

6) Using the Binomial Distribution
formula find the probability that a family that has 13
children has 10 girls.

Answer #1

1. There are 4 queens in a deck of 52 cards.

Probability that the first card is a queen = 4/52. After the first queen is drawn, there are now 3 queens in the deck of 51 cards

Probability that the next card is a queen = 3/51

Probability that the first 2 cards are queens = (4/52) x (3/51) = 0.0045

2. Assuming that each book is unique, 4 books can be selected from 12 book set in 12 x 11 x 10 x 9 = 11880 ways.

3. The chairperson can be selected in 15 ways, president in 14 ways, secretary in 13 ways and treasurer in 12 ways.

Total no. of possible combinations = 15 x 14 x 13 x 12 = 32760

4. Part of this question is missing.

Suppose that from a standard deck of cards you draw three cards
without replacement.
(a) Let X be the number of queens among your three cards. Complete
the probability distribution for X shown below.
X
0
1
2
3
P(X)
(b) What is the expected number of queens that you will draw?

Three cards are drawn from a deck without replacement.
Find the probability the first card is a club, the second card
is a heart, and the third card is a black card.
Let A = 1st club Let B = 2nd heart Let C = 3rd black card
P( 1st club and 2nd heart and 3rd black card )
Write Answer as a Fraction (Not Simplified)
Write Answer as a Percent Round to Two Decimal Places =

Two cards are selected at random from a standard 52-card deck
without replacement. Find the probability the first card is the 7
of Diamonds (♦) and the second card is a Club (♣).
Give your answer as a decimal rounded to 4 decimal places

Two cards are drawn without replacement from a standard deck of
52 playing cards. What is the probability of choosing a face card
for the second card drawn, if the first card, drawn without
replacement, was a jack? Express your answer as a fraction or a
decimal number rounded to four decimal places.

1. If two cards are drawn at random in succession from a
standard 52-card deck without replacement and the second card is a
club card, what is the probability that the first card is king
card?
2. Let A and B be two events in a sample S. Under what
condition(s) is P(A l B) equal to P(B l A) ?
3. If two events A and B are mutually Exclusive. Can A and B be
Independent? Why or why...

A standard deck of playing cards has exactly 52 cards (not
counting jokers). Of the 52 cards, 4 are kings and 4 are queens. If
five cards are dealt from a shuffled deck, what is the probability
of getting exactly 2 kings and exactly 1 queen?

We draw cards, one by one, without replacement, from a deck of
52 cards. Calculate the probability that the first ace will appear
in the k-th draw, if we know that the n-th card was a spade, and
the m-th card was not a club. k=42,m=18,n=4

Suppose two cards are drawn at random from a standard deck. Find
the probability that both cards are queens given both are face
cards.

Suppose two cards are drawn in succession (without replacement)
from a standard deck of cards.
What is the probability that a face card is drawn first? (Enter
your probability as a fraction.)
What is the probability that a face card is drawn second, given
that a face card was drawn first? (Enter your probability as a
fraction.)
What is the probability of drawing two cards in succession
(without replacement) from a standard deck and having them both be
face cards?...

Five cards are drawn without replacement from a standard deck of
52 cards consisting of four suits of thirteen cards each. Calculate
the probability that the five cards result in a flush (all five
cards are of the same suit).

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