Question

You draw two cards from a standard deck of 52 cards without replacing the first one...

You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second.

(a) Are the outcomes on the two cards independent? Why?

Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.Yes. The events can occur together.    No. The events cannot occur together.No. The probability of drawing a specific second card depends on the identity of the first card.


(b) Find P(3 on 1st card and 10 on 2nd). (Enter your answer as a fraction.)


(c) Find P(10 on 1st card and 3 on 2nd). (Enter your answer as a fraction.)


(d) Find the probability of drawing a 10 and a 3 in either order. (Enter your answer as a fraction.)

Homework Answers

Answer #1

a)

two outcomes will be independent , if outcome of one does not effect other,but

here, cards are drawn without replacement,so, probability of second card get effected,so, answer is

No. The probability of drawing a specific second card depends on the identity of the first card.

b)when first card is drawn , total cards left = 51

Find P(3 on 1st card and 10 on 2nd) = P(3 on first)*P(10 on 2nd | 3 on first) = 4/52 * 4/51 = 4/663

c)

P(10 on 1st card and 3 on 2nd) = 4/52 * 4/51 = 4/663

d)

probability of drawing a 10 and a 3 in either order = P(3 on first)*P(10 on 2nd | 3 on first) + P(10 on 1st card and 3 on 2nd) = 4/663 + 4/663 = 8/663

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The following question involves a standard deck of 52 playing cards. In such a deck of...
The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four...
The following question involves a standard deck of 52 playing cards. In such a deck of...
The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four...
he following question involves a standard deck of 52 playing cards. In such a deck of...
he following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four...
home / study / math / statistics and probability / statistics and probability questions and answers...
home / study / math / statistics and probability / statistics and probability questions and answers / The Following Question Involves A Standard Deck Of 52 Playing Cards. In Such A Deck Of Cards ... Question: The following question involves a standard deck of 52 playing cards. In such a deck of cards ther... (2 bookmarks) The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards...
Lacy draws a diamond from a standard deck of 52 cards. Without replacing the first card,...
Lacy draws a diamond from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card and gets a club. Are these events independent? Input Yes or No: Determine the probability of drawing a diamond and then a club without replacement. Write your answer in decimal form, rounded to four decimal places as needed. Answer = Linda draws a diamond from a standard deck of 52 cards. She returns the diamond to...
Please show work in detail and explain all steps General: Deck of Cards You draw two...
Please show work in detail and explain all steps General: Deck of Cards You draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the f rst one back and reshuff e the deck. (a) Are the outcomes on the two cards independent? Why? (b) Find P(3 on 1st card and 10 on 2nd). (c) Find P(10 on 1st card and 3 on 2nd). (d) Find the probability of drawing a...
Suppose two cards are drawn in succession (without replacement) from a standard deck of cards. What...
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?...
Sara draws the 4 of hearts from a standard deck of 52 cards. Without replacing the...
Sara draws the 4 of hearts from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card. a. Determine the probability that the second card is another 4. P(4∣4 of hearts) = b. Determine the probability that the second card is another heart. P(P(heart ∣ 4 of hearts) = c. Determine the probability that the second card is a club. P(P(club ∣ 4 of hearts) = d. Determine the probability that...
Three cards are drawn from a deck without replacement. Find the probability the first card is...
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 =
You are dealt two cards successively without replacement from a standard deck of 52 playing cards....
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.