Question

1.

a.) Suppose you draw 8 cards from a standard deck of 52 cards, one after the other, without replacement. Find the probability that the last card is a club given that the first 7 cards are clubs.

b.) An urn contains 6 green, 10 blue, and 17 red balls. You take 3 balls out of the urn, one after the other, without replacement. Find the probability that the third ball is green given that the first two balls were red.

c.) You roll two fair dice. Find the probability that the first die is a 6 given that the minimum of the two numbers is a 5.

d.) You toss a fair coin 7 times. Find the probability of no more than 6 heads given that at least one toss resulted in heads.

2.

a.) A bag contains 2 coins, one fair and the other with 2 heads. You pick 1 coin at random and flip it. What is the probability that you picked the fair coin given that the outcome of the toss was heads?

b.)You pick 2 cards from a standard deck of 52 cards. Find the probability that the first card was a heart given that the second card was a heart.

c.) A drawer contains six bags numbered 1-6, respectively. Bag
*i* contains *i* blue balls and 5 green balls. You
roll a fair die and then pick a ball out of the bag with the number
shown on the die. What is the probability that the ball is
blue?

Answer #1

1.
a.) Suppose you draw 5 cards from a standard deck of 52 cards,
one after the other, without replacements. Find the probability
that the last card is a club given that the first 4 are clubs.
b.) A drawer contains six bags numbered 1-6, respectively i
contains i blue balls and 6 green balls. You roll a fair die and
then pick a ball out of a bag with the number shown on the die.
What is the probability...

1. Two cards are drawn from a well-shuffled ordinary
deck of 52 cards. Find the probability that they are both aces if
the first card is (a) replaced, (b) not replaced.
2. Find the probability of a 4 turning up at least once in two
tosses of a fair die.
3. One bag contains 4 white balls and 2 black balls; another
contains 3 white balls and 5 black balls. If one ball is drawn from
each bag, find the...

From a deck of 52 cards, what is the probability that you draw a
face card (J,Q,K), an Ace or a black card?
2. If you flip a coin 5 times and 4 times you see a head, what
is the probability that the next flip is a tail?
3. Using 2 eight-side dice, what is the probability that you
roll the most common combined number?
4. What is the probability that you roll 2 consecutive green
numbers (i.e., 0,00)...

You draw 2 cards from a standard deck of cards without
replacement.
1) What is the probability that the second card is a queen given
that the first card is a jack?
2) What is the probability that the second card is red given
that the first card was a heart?
3) What is the probability that the second card is red given
that the first card is red?

A standard deck of cards contains 52 cards. One card is selected
from the deck. (a) Compute the probability of randomly selecting a
a heart heart or club club. (b) Compute the probability of
randomly selecting a a heart heart or club club or diamond diamond.
(c) Compute the probability of randomly selecting an an ace ace or
heart heart.

2. A card is chosen from a deck of cards. If it is a 9 or a 10,
you choose a ball from box 1. Otherwise you choose a
ball from box 2. Box 1 contains 4 blue balls and 9 white balls. Box
2 contains 4 white balls and 7 blue balls. What is the probability
that you end up with a blue ball? (3)

a) f you randomly select two cards from a deck of playing cards
without replacement, what is the probability that you get an ace
card followed by a face card
b) if you toss a coin 400 times, find the usual range for the
number of tails that you expect to get.
c) Find the probability of selecting at least 1 ace card when
you draw 3 cards without replacement. Answer in reduced
fraction.
d) Given x̅ = 78.5 and...

1. Suppose you draw two cards from a deck of 52 cards without
replacement.
a. What’s the probability that the ﬁrst draw is a heart and the
second draw is not a heart?
b. What’s the probability that exactly one of the cards are
hearts?
c. If you draw two cards with replacement, what’s the
probability that none of the cards are hearts?

Suppose you are about to draw two cards at a random from a deck
of playing cards. Note that
there are 52 cards in a deck. Find the following
probabilities.
a. What is the probability of getting a Jack and then a King
(with replacement)?
b. What is the probability of getting a Heart or Jack and then a
2 (with replacement)?
c. What is the probability of getting an Ace and then a Queen
(without replacement)?
d. What is...

An urn contains 6 green ball, 7 blue balls and 5 yellow balls.
You are asked to draw 3 balls, one at a time (without replacement).
Find the probability that a green is pulled first, then another
green ball then a blue ball.

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