A card game is played with a deck of 6 cards which can be one of 2 suits, one of the suits being hearts, and one of ranks. A hand is a subset of 3 cards. What is the probability that a hand has exactly two hearts? 9/20 # What is the probability that a hand has exactly two hearts given that it has at least one heart? (3/20) Hint: use the formula for conditional probability. The denominator, the probability that the hand has at least one hear can be computed using complements. The numerator is the probability that the hand has exactly two hearts and it has at least one heart, so it has exactly ??? hearts. What is the probability that a hand has exactly two hearts given that it has the 2 of hearts? 0.6 ⠀ Hint: try restricted sample spaces. For the denominator, use two stages: count hands that have one specific card, the 2 of hearts, and a subset of any two cards from the rest of the deck. The numerator is the number of hands that have exactly two hearts, with one of them being the 2 of hearts. Try thre stages: pick the 2 of hearts, then pick another heart, then pick a third card that is not a heart.

A card game is played with a deck of 6 cards which can be one of 2 suits, one of the suits being hearts, and one of ranks. A hand is a subset of 3 cards. What is the probability that a hand has exactly two hearts? 9/20 # What is the probability that a hand has exactly two hearts given that it has at least one heart? (3/20) Hint: use the formula for conditional probability. The denominator, the probability that the hand has at least one hear can be computed using complements. The numerator is the probability that the hand has exactly two hearts and it has at least one heart, so it has exactly ??? hearts. What is the probability that a hand has exactly two hearts given that it has the 2 of hearts? 0.6 ⠀ Hint: try restricted sample spaces. For the denominator, use two stages: count hands that have one specific card, the 2 of hearts, and a subset of any two cards from the rest of the deck. The numerator is the number of hands that have exactly two hearts, with one of them being the 2 of hearts. Try thre stages: pick the 2 of hearts, then pick another heart, then pick a third card that is not a heart.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram.…

A: Given information is shown in the even diagram

Q: You and your friend are rolling a die. Assuming the dies is fair and six sided, calculate the…

A: For equally likely outcomes, the probability of favorable events can be given by the ratio of number…

Q: Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram.…

Q: A local high school has both male and female students. Each student either plays a sport or doesn't.…

A: sport no sport total male 12 8 20 female 20 10 30 total 32 18 50

Q: The spinner is spun one time. Find the probabilities. A A A B.

A: Let U be the union of the set U={A,A,A,B,B,C,D,E} n(U)=8, n(A)=3, n(B)=2, n(C)=1,n(D)=1,n(E)=1…

Q: (a) P(A U B) = 0.74 (Simplify your answer.) (b) The odds in favor of A are (Simplify your answer.…

A: It is given that P(A) = 0.35 P(B) = 0.6 P(A∩B) = P(A and B) = 0.23 Note: According to Bartleby…

Q: Focus on the ‘Big Wheel’ problem from the Price is Right. With knowing how to calculate whether or…

A: Given the ‘Big Wheel’ problem probabilities to calculate whether or not the final contestant will…

Q: Which of the following values cannot be probabilities? 3/5, -0.5, √2, 0.09, 5/3, 0, 1, 1.23 Select…

A: probability define as The ratio of the number of favorable outcomes to certain event and total…

Q: Which of the following values cannot be probabilities?…

A: Concept of probability:Probability deals with the likelihood of occurrence of a given event. The…

Q: Some friends are playing a game in which two 12-sided number cubes are rolled. One of them…

A: If two fair 12 sided dice are rolled then the total possible outcomes = 12*12 = 144 The sum of two…

Q: Calculate the probabilities labeled on the tree diagram. (Give answers correct to four decimal…

Q: 49. It is estimated that 63% of Americans will watch the Masters golf tournament and only 48% will…

Q: Use the two-way table to answer the questions that follow

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: 3. | Statistical Literacy What is the probability of (a) an event A that is certain to occur? (b) an…

A: Probability tells about the chance for an event to occur. It ranges from 0 to 1.

Q: One coin in a collection of 13 is rigged to have a probability of showing heads equal to 0.6. The…

A: et R shows the event that a rigged coin is selectedand F shows the event that a fair coin is…

Q: ave to show all work to receive credit and probabilities must be written properly. For example:…

A: Probability indicates the chances of occurring an even. It lies between 0 and 1. It is given that,…

Q: 28% of college students say they use credit cards because of the rewards program. You randomly…

A: Givenp=0.28n=10Let "x" be the no.of students say they use credit…

Q: 10% of all computers are infected with a computer virus. A company's virus-detection software…

A: Here we will use Bayes theorem to find solution .So 1sy we will make a tree diagram for all data…

Q: Bridget is registering for a reading class. Below is a table of teachers and the periods they teach…

A: There are total number of classes N= 9. Bridget prefers either Professor Plum or Mr. Green. The…

Q: Reaction time is normally distributed, with a mean of 0.6 sec and a standard deviation of 0.1 sec.…

A: Let, X= reaction time Given X follows a normal distribution with mean = 0.6 and standard deviation=…

Q: because the probabilities do not depend on When flipping coins, we say the outcomes are previous…

A: Given: Probability of flipping coin: The total number of possible outcomes when coin is toss=2=n(S)…

Q: If you viewed Attend as a Child as the Independent Variable, conditional probabilities should be…

A: if we view "Attend as a child" as the independent variable, conditional probabilities should be…

Q: oll a pair of dice 100 times. Keep a record of the sums of the dice. Find the theoretical…

Q: Two fair six-sided. diamond are rolled. What is the probabilities that the some of the two side is…

Q: Refer to the contingency table shown below smoking by race aged 18 to 24 white 278, 555, 833 black…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts for…

Q: Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram.…

A: it is given that, P(A)=0.43 P(B)=0.52 P(A and B) =0.05

Q: Choose the correct answer below. O A. The statement does not make sense because an event having two…

A: It might be rai tomorrow or it might not be rain tomorrow, is a statement. So, if one says that…

Q: A box has four red balls numbered 0 - 3 and six black balls numbered 4 - 9. Let A be the event that…

Q: Roll a pair of dice 100 times. Keep a record of the sums of the dice. Find the theoretical…

A: If a dice is thrown twice then there are total 6*6 = 36 possible outcomes. So, P(x) = number of ways…

Q: Which of the following values cannot be probabilities? 0.03, v2, 1, - 0.51, 0, 3/5, 5/3, 1.13 Select…

Q: Which of the following values cannot be probabilities? 1, 2,5/3,-0.46, 0.03, 0, 1.53, 3/5 Select all…

Question

100%

Need help calculating probabilities.

A card game is played with a deck of 6 cards which can be one of 2 suits, one of the suits being hearts, and one of 3
ranks. A hand is a subset of 3 cards.
What is the probability that a hand has exactly two hearts?
9/20
What is the probability that a hand has exactly two hearts given that it has at least one heart?
(3/20)
T
Hint: use the formula for conditional probability. The denominator, the probability that the hand has at least one heart,
can be computed using complements. The numerator is the probability that the hand has exactly two hearts and it
has at least one heart, so it has exactly ??? hearts.
What is the probability that a hand has exactly two hearts given that it has the 2 of hearts?
0.6
T
T
Hint: try restricted sample spaces.
For the denominator, use two stages: count hands that have one specific card, the 2 of hearts, and a subset of any
two cards from the rest of the deck.
The numerator is the number of hands that have exactly two hearts, with one of them being the 2 of hearts. Try three
stages: pick the 2 of hearts, then pick another heart, then pick a third card that is not a heart.

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given Information:

VIEW

Step 2: Find the probability that a hand has exactly two hearts:

VIEW

Step 3: Find the probability that a hand has exactly two hearts given that it has at least one heart:

VIEW

Step 4: Find the probability that a hand has exactly two hearts given it has 2 of hearts:

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 18 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Which of the following values cannot be probabilities? 1, 5/3, 3/5, 2, 0.07, 1.44, −0.53, 0 Question content area bottom Part 1 Select all the values that cannot be probabilities.
You are considering participating in the student math league which offers cash prizes for certain score on the test. After researching results in the past you estimate that there is a 1/120 chance you will win $100, a 1/60 chance you will win $50, a 1/22 chance you will win $25, and a 1/9 chance you will win $10. Fill in the table below, with the prizes in order starting with the largest. Write the probabilities as decimals rounded to four decimal places and round monetary amounts to the nearest cent. Prize Probability Product $ $ $ $ $ $ $ $ $ $
I'm having trouble with probabilities. To be more specific it starts with the three terms of 1) Actual Odds Against, 2) Actual Odds in Favor, and 3) Payoff Odds. I read the material and watched videos but can't seem to grasp the material.
write properly
All probabilities can be expressed as decimal values ranging from 0.00 to 1.00. O True O False
Which of the following values cannot be probabilities? 0, 5/3, 3/5, 1, - 0.53, 1.16, 0.01, 2 Select all the values that cannot be probabilities. OA. 2 O B. - 0.53 O C. 0 O D. 0.01 O E. 3 F. 1.16 O G. 1 H. 5
Suppose we know that the probabilities P(A) = .5, P(B|A) = .3 and P(A or B) =.3. What is the value for P(A and B)? What is the value for P(B)?
Please help me solve the rest.
Detailed below is one of the nefarious dicing practices of the Win Some/Lose Some Casino. HINT [See Example 3.] Some dice are specially designed so that 1 comes up a fourth of the time, 6 never comes up, and all the other outcomes are equally likely. Find the probabilities of all the possible outcomes. (Enter your probabilities as fractions.) Outcome 1 2 3 4 5 6 Probability Find the probability that an odd number faces up.
Which of the following values cannot be probabilities? 1, 1.49, 0.09, 3/5, 0, 5/3, - 0.45, /2 Select all the values that cannot be probabilities. O A. 1.49 O B. 0.09 O C. 5 3 O D. 1 O E. - 0.45 OF. V2 O G. 3 O H. 0
please 19a,19b thank you