Question: Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart." If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?

(A) 1/4
(B) 1/5
(C) 5/26
(D) 12/42
(E) 13/42

Correct Answer: A
Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

• Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart."
• Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck.

Find Out:

• The probability that the 10th card dealt is a heart.

As per the condition of the question, desired outcomes= 13
Total outcomes= 52
Probability of getting any card as the heart card= 13/52= 1/4
It will be the same probability for the 10th card as well.

Therefore, the probability that the 10th card dealt is a heart = 1/4.

Approach Solution 2:

The problem statement informs that:

Given:

• Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart."
• Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck.

Find Out:

• The probability that the 10th card dealt is a heart.

Let us use the concept of reverse probability to solve the above mentioned problem.
The probability that the 10th card drawn is a heart will be the same as (1- the probability that the 10th card drawn is not a heart)
Let us denote the probability that the 10th card drawn is not heart as P(Not H) and the probability that the 10th card drawn is heart as P(H)

Then, P(H) = 1- P (Not H)

Now the 10th card has 39 options if it is not a heart.

Hence, P (Not H) = 39/52
Or, P (Not H) = 3/4
So, P(H) = 1 - 3/4
Or, P(H) = 1/4

Therefore, the probability that the 10th card dealt is a heart = 1/4.

Approach Solution 3:

The problem statement implies that:

Given:

• Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart."
• Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck.

Find Out:

• The probability that the 10th card dealt is a heart.

Let us use the approach of permutation and combination to solve the problem.
We can see the problem in the following way:

Our required probability = (Total no. of ways in which the 10th card is a heart) / (Total no. of ways in which the 10th card can be drawn)

The total no. of ways in which the 10th card can be drawn is (\(^{52}C_1\) ) which is equal to
52! / [1!*(52-1)!] = 52! / [1*51!] = 52
Please note that we have used the formula (\(^nC_r\) ) = n!/ [r! * (n-r)!]

Similarly, the numerator will be the total no. of ways in which the 10th card is a heart (\(^{13}C_1\) ) which is equal to 13! / [1!*(13-1)!] = 13! / [1*12!] = 13
Hence, the required probability is 13/52
The probability that the 10th card drawn is 13/52 i.e. 1/4

Therefore, the probability that the 10th card dealt is a heart = 1/4.

“Laura has a deck of standard playing cards with 13 of the 52 cards”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions help the candidates to improve their mathematical knowledge in order to crack numerical problems. GMAT Quant practice papers assist the candidates to analyse varieties of questions that will enable them to score better in the GMAT exam.

Suggested GMAT Problem Solving Samples

• Which of the Following is Equal to the Value of 2^5+2^5+3^5+3^5+3^5 ? GMAT Problem Solving
• The Price of a Certain Painting Increased By 20% During the First Year GMAT Problem Solving
• The Population of the Village is 5500. If the Number of Males Increase GMAT Problem Solving
• Machine A Produces 100 Parts Twice as Fast as Machine B does GMAT Problem Solving
• The Difference Between a Two-Digit Number and the Number Obtained GMAT Problem Solving
• Which of the following is always equal to sqrt(9+x^2-6x)?GMAT Problem Solving
• A Colony has Houses Numbered 1 to 150 GMAT Problem Solving
• Two Vessels A and B Contain Milk and Water Mixed in the Ratio 8:5 GMAT Problem Solving
• A Dealer Offers a Cash Discount of 20%. Further, a Customer Bargains GMAT Problem Solving
• If a Regular Hexagon is Inscribed in a Circle with a Radius of 4, The GMAT Problem Solving
• There are Two Vessels A and B. Vessel A is Containing 40 Litres of GMAT Problem Solving
• At A Certain Fruit Stand, The Price Of Each Apple Is 40 Cents GMAT Problem Solving
• The Coordinates Of Vertices P And Q Of An Equilateral Triangle PQR Are GMAT Problem Solving
• A Certain Roller Coaster has 3 Cars, and A Passenger is Equally Likely GMAT Problem Solving
• A Manufacturer Produces a Certain Men's Athletic Shoe in GMAT Problem Solving
• In The Figure Shown Below, The Area of Square Region ACEG is 729 GMAT Problem Solving
• How Many Dimes are There in 4x - 1 Cents? (1 dime = 10 cents) GMAT Problem Solving
• In How Many Ways The Letter Of The Word "Family" Can Be When GMAT Problem Solving
• A Fair Coin Is Tossed 4 Times. What Is The Probability Of Getting At GMAT Problem Solving
• In A Sequence 1, 2, 4, 8, 16, 32, ... Each Term After The First Is Twice GMAT Problem Solving
• What Is The Sum Of Odd Integers From 35 To 85, Inclusive? GMAT Problem Solving
• If x = -3, What Is The Value Of -3x^2? GMAT Problem Solving
• If 2p + 1/p = 4, Then what is the Value of p^3 + 1/8p^3 ? GMAT Problem Solving
• There are 12 Pipes that are Connected to a Tank. Some of them are fill GMAT Problem Solving
• A wire is cut into three equal parts. The resulting segments are then cut GMAT Problem Solving
• There Were R Red Balls And Y Yellow Balls In A Bag. Three Red Balls GMAT Problem Solving
• With An Average Speed Of 40 Km/H, A Train Reaches Its Destination On GMAT Problem Solving
• A Photographer Will Arrange 6 People Of 6 Different Heights GMAT Problem Solving
• What Is The Radius Of The Incircle Of The Triangle Whose Sides Measure GMAT Problem Solving
• The Value Of (2^(-14) + 2^(-15) + 2^(-16) + 2^(-17))/5 Is GMAT Problem Solving
• Points A And B Are 120 Km Apart. A Motorcyclist Starts From GMAT Problem Solving
• A student took five papers in an examination, where the full marks GMAT Problem Solving
• In how many ways can letters the word ATTITUDE be rearranged such that GMAT Problem Solving
• A merchant mixes three varieties of rice costing $20/kg, $24/kg GMAT Problem Solving
• ABC is an equilateral triangle, and point D is the midpoint of side BC GMAT Problem Solving
• A Batsman Makes a Score of 87 Runs in the 17th Match and Thus Increases GMAT Problem Solving
• If M= √4+3√4+4√4, Then the Value of M is GMAT Problem Solving
• An Octagon Is Inscribed In A Circle As Shown Above. What Of The Area GMAT Problem Solving
• In a Company of Only 20 Employees, 10 Employees make $80,000/yr GMAT Problem Solving
• A bag contains blue and red balls only GMAT Problem Solving
• (4.8*10^9)^(1/2) is closest in value to GMAT Problem Solving
• What Is The Units Digit Of 2222^333 ∗ 3333^222? GMAT Problem Solving
• What Is The Tens Digit Of 6^17? GMAT Problem Solving
• If m=−2, What Is −m^(−m)? GMAT Problem Solving
• An Automated Manufacturing Plant Uses Robots To Manufacture Products GMAT Problem Solving
• The Surface Distance Between 2 Points on the Surface of a Cube is the GMAT Problem Solving
• The Average Monthly Expenditure of a Family for the First Four Months GMAT Problem Solving
• When a Certain Perfect Square is Increased by 148, the Result is GMAT Problem Solving
• If p#q Denotes the Least Common Multiple of p and q, Then ((12#16) GMAT Problem Solving
• In How Many Ways Can One Divide 12 Different Chocolate Bars Into Four GMAT Problem Solving