Question

4. You pick cards one at a time without replacement from an ordinary deck of 52 playing cards. What is the minimum number of cards you must pick in order to guarantee that you get

a) a pair of any kind,

b) a pair of Kings, and

c) all four Kings.

5. Use the binomial theorem to expand (x + 3y)4 . You must illustrate use of the binomial theorem

Answer #1

1. (4 pts) Consider all bit strings of length six. a) How many
begin with 01? b) How many begin with 01 and end with 10? c) How
many begin with 01 or end with 10? d) How many have exactly three
1’s? 2. (8 pts) Suppose that a “word” is any string of six letters.
Repeated letters are allowed. For our purposes, vowels are the
letters a, e, i, o, and u. a) How many words are there? b)...

Question 2. A standard deck of playing cards has 52 cards, 4 of
which are kings. What is the probability of not getting four kings
if you draw 4 cards without putting the cards back into the
deck?
Please show your workings, not just the answer, thank you!

If 13 cards are to be chosen at random (without replacement)
from an ordinary deck of 52 cards, find the probability that
(a) 6 will be picture cards.

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.

Suppose three cards are randomly selected (without
replacement) from a standard deck of 52 cards.
a) What is the probability of getting three aces? Ans:
0.00018
b) What is the probability of getting a pair? (Do not count
three of a kind.)
c) What is the probability that they all have the same
suit?

You are dealt two cards successively without
replacement from a standard deck of 52 playing cards.
Find the probability that the first card is a king and the
second card is a queen.
I want the probability that both events will
occur. I do not want the probability of each
event.

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).

A standard deck consists of 52 cards of which 4 are aces, 4 are
kings, and 12 (including the four kings) are "face cards" (Jacks,
Queens, and Kings). Cards are dealt at random without replacement
from a standard deck till all the cards have been dealt. Find the
expectation of the following. Each can be done with almost no
calculation if you use symmetry.
a) The number of aces among the first 5 cards
b) The number of face cards...

If 2 cards are selected from a deck of 52 cards
without replacement, find the probability of both are the same
color

You have a deck of 52 playing cards you are dealt 4
cards. What is the probability you are dealt exactly one
pair?

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