Question

Suppose that you have 9 green cards and 5 yellow cards. The cards are well shuffled. You randomly draw two cards with replacement. Round your answers to four decimal places. G1 = the first card drawn is green G2 = the second card drawn is green

a. P(G1 and G2) =

b. P(At least 1 green) =

c. P(G2|G1) =

d. Are G1 and G2 independent?

They are independent events

They are dependent events

Answer #1

Total number of cards: 9+5 = 14

Out of 14 cards, 9 cards are green. Since draws are done with replacement so probability of getting green card remain same each time. The probability of getting green card in first draw is

P(G1) = 9/14

And likewise

P(G2 | G1) = 9/14

(a)

P(G1 and G2) = P(G2 | G1) * P(G1) = (9/14) * (9/14) = 81 / 196 = 0.4133

(b)

The probability no card is green is

P(no green) = (5/14) * (5/14) = 25 /196

So the probability that at least 1 green is

P(at least 1 green) = 1 - P(no green) = 1 - 25/196 = 171 /196 = 0.8724

(c)

P(G2 | G1) = 9/14

(d)

Yes they are independent because draws are with replacement.

Suppose that you have 9 cards. 4 are red and 5 are purple. The
cards are well shuffled. You randomly draw two cards
without replacement. (card is not returned to the
pile after being drawn.) Justify your answers in the scratch work
file.
Define the following events:
R1 = first card drawn is red
R2 = second card drawn is red
Find the following probabilities: *round answers to two decimal
places*
P(R1 AND R2) = ______
P(At least one red)...

Suppose that you have 9 cards. 6 are green and 3 are yellow. The
6 green cards are numbered 1, 2, 3, 4, 5, and 6. The 3 yellow cards
are numbered 1, 2, and 3. The cards are well shuffled. You randomly
draw one card.
• G = card drawn is green
• Y = card drawn is yellow •
E = card drawn is even-numbered
a. List the sample space. (Type your answer using letter/number
combinations separated by...

A special deck of cards has 5 green cards , and 3 yellow cards.
The green cards are numbered 1, 2, 3, 4, and 5. The yellow cards
are numbered 1, 2, and 3. The cards are well shuffled and you
randomly draw one card.
G = card drawn is green
E = card drawn is even-numbered
a. How many elements are there in the sample space?
b. P(E) = __________________ (Round to 4 decimal places)

A special deck of cards has 5 green cards , and 3 yellow cards.
The green cards are numbered 1, 2, 3, 4, and 5. The yellow cards
are numbered 1, 2, and 3. The cards are well shuffled and you
randomly draw one card.
G = card drawn is green
E = card drawn is even-numbered
a. How many elements are there in the sample
space?
b. P(E) = (Round to 4 decimal places)

A special deck of cards has 5 green cards , and 3 yellow cards.
The green cards are numbered 1, 2, 3, 4, and 5. The yellow cards
are numbered 1, 2, and 3. The cards are well shuffled and you
randomly draw one card.
G = card drawn is green
E = card drawn is even-numbered
a. How many elements are there in the sample
space? _____
b. P(E) =_____ (Round to 4 decimal places)
2. A special deck of cards...

5. J and K are independent events. P(J | K) = 0.7. Find
P(J).
6. Suppose that you have 10 cards. 6 are green and 4 are
yellow. The 6 green cards are numbered 1, 2, 3, 4, 5, and 6. The 4
yellow cards are numbered 1, 2, 3, and 4. The cards are well
shuffled. You randomly draw one card.
• G = card drawn is green
• Y = card drawn is yellow
• E = card...

Two cards are drawn successively from an ordinary deck of 52
well-shuffled cards. Find the probability that a. the first card is
not
a Four of Clubs or an Five;
b. the first card is an King but the second is not;
c. at least one card is a Spade;

Two cards are drawn without replacement from a well shuffled
deck of cards. Let H1 be the event that a heart is drawn first and
H2 be the event that a heart is drawn second. The same tree diagram
will be useful for the following four questions. (Note that there
are 52 cards in a deck, 13 of which are hearts)
(a) Construct and label a tree diagram that depicts this
experiment.
(b) What is the probability that the first...

Assume an ordinary deck of 52 cards that has been
well-shuffled.
1. What is the probability of drawing an eight and then drawing
another eight assuming the first card is put back in the deck
before the second draw?
2. What is the probability of drawing an eight and then drawing
another eight assuming the first card is NOT put back in the deck
before the second draw?
3. What is the probability of drawing at least one card that...

Consider the following
experiment. Four cards are drawn out of a deck with
replacement from a well-shuffled deck of cards. The card
that is drawn out is either a heart or it is not a
heart. After a card is drawn out and recorded it is put
back into the deck and the deck is
reshuffled. Construct the binomial probability
function for x = 0, 1, 2, 3, 4
P(0) =
P(1) =
P(2) =
P(3) =
P(4) =

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 13 minutes ago

asked 14 minutes ago

asked 15 minutes ago

asked 15 minutes ago

asked 18 minutes ago

asked 23 minutes ago

asked 30 minutes ago

asked 37 minutes ago

asked 56 minutes ago

asked 1 hour ago

asked 1 hour ago