Question: A briefcase lock is a combination of 4 digits where each digit varies from 0 to 9. If a person tries any combination randomly then what is the probability that he puts atleast 2 digits right but is unable to unlock the briefcase?

1. 0.0544
2. 0.0562
3. 0.0522
4. 0.0564
5. None of these

Answer:
Approach Solution (1):

Case 1: 2 digits correct:
----: Is the code. We want 2 digits at the correct place, but there are 4 places available for these 2 digits. So, we have to select two places, i.ie. 4C2 = 6
For the remaining two digits we have 9 digits to choose form. As the 10th digit will definitely be correct.
So the total combinations = 6 * 9 * 9 = 486

Case 2: 3 digits correct:
----: Is the code. We want 3 digits at the correct place, but there are 4 places available for these 3 digits. So, we have to select 3 places, i.ie. 4C3 = 4
For the remaining two digits we have 9 digits to choose form. As the 10th digit will definitely be correct.
So the total combinations = 4 * 9 = 36
Total favorable cases = 486 + 36 = 522
Total cases = 10,000
Probability = 0.0522

Correct option: C

Approach Solution (2):

Total number of ways in which the 4 digits can be put = 10 * 10 * 10 * 10 =\(10^4\)
There are two cases:
(1) The one in which 2 are correct and 2 are incorrect:
2 correct: 1 * 1
2 incorrect: 9 * 9
Selecting 2 places out of 4: 4C2 = 6
Therefore probability =\(\frac{6*1*1*9*9}{10^4}=0.0486\)

(2) The one in which 3 are correct and 1 is incorrect:
3 correct: 1 * 1 * 1
1 incorrect: 9
Selecting 3 places out of 4 for incorrect or 1 place out of 4 correct: 4C3 or 4C1 = 4
Therefore probability = \(\frac{4*1*1*1*9}{10^4}=0.0036\)
Taking sum of the above two independent probabilities = 0.0486 + 0.0036 = 0.0522

Correct option: C

Approach Solution (3):
We can deduct the probabilities of 1 right 3 wrong, 4 right and 4 wrong from 1:
(1) 1R3W =\(\frac{1}{10}*(\frac{9}{10})^3*4\)
(2) 4R =\(\frac{1}{10000}\)
(3) 4W =\((\frac{9}{10})^4\)
Adding the above 3 cases:\(\frac{9478}{10000}\)
Hence 1 -\(\frac{9478}{10000}\)=\(\frac{522}{10000}=0.0522\)

Correct option: C

“A briefcase lock is a combination of 4 digits where each digit varies from 0 to 9. If a person tries any combination randomly then what is the probability that he puts atleast 2 digits right but is unable to unlock the briefcase?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Suggested GMAT Problem Solving Questions:

• If 10 Millimeters Equal 1 Centimeter, How many Square Centimeters does 1 Square Millimeter Equal? GMAT Problem Solving
• Assume that all 7-Digit Numbers That do not Begin with 0 or 1 are Valid Phone Numbers. GMAT Problem Solving
• A Contractor Estimated that his 10-Man Crew Could Complete the Construction in 110 Days if There Was no Rain. GMAT Problem Solving
• GMAT Problem Solving - How Much Pure Alcohol Should Be Added To 400 ml of a 15% Solution To Make The Strength Of The Solution 32%?
• Find The Altitude Of An Equilateral Triangle Whose Side is 20 GMAT Problem Solving
• Which of the following is the value of √3√0.000064? GMAT Problem Solving
• GMAT Problem Solving – If @ x=x^2/2x^2-2 , What is the Units Digit of @ (@4)?
• GMAT Problem Solving – What is the product of all possible solutions of the equation |x+2|- 5|x+2| = -6?
• A Welder Received an Order to Make a 1 Million Litre Cube-Shaped Tank. GMAT Problem Solving
• A Right Angled Triangle has its Sides in Arithmetic Progression and Being Integers GMAT Problem Solving
• What is the Largest Power of 3 Contained in 200! GMAT Problem Solving
• If g is an integer what is the value of\((-1)^{g^{4-1}}\)?GMAT Problem Solving
• If @\(x=\frac{x^2}{2x^2}-2\), What is the Units Digit of @(@4)? GMAT Problem Solving
• GMAT Problem Solving - Iqbal Dealt Some Cards to Mushtaq and himself from a Full Pack of Playing Cards
• Running at the Same Constant Rate, 6 Identical Machines GMAT Problem Solving
• A conference room is equipped with a total of 45 metal or wooden chairs GMAT Problem Solving
• The Greatest 6-Digit Number When Divided by 6, 7 ,8 , 9, and 10 Leaves a Remainder of 4, 5, 6, 7, and 8 Respectively GMAT Problem Solving
• The square of 5√2 =?GMAT Problem Solving
• If \(x^2\)=\(2^x\), What is the Value of x ?GMAT Problem Solving
• A Shop Stores x kg of Rice. The First Customer Buys half this Amount Plus half a kg of Rice GMAT Problem Solving
• In a Class of 120 Students Numbered 1 to 120, All Even Numbered Students Opt for Physics GMAT Problem Solving
• Machine A Produces bolts at a Uniform Rate of 120 Every 40 seconds GMAT Problem Solving
• Out of 7 Consonants and 4 Vowels, How Many Words of 3 Consonants and 2 Vowels Can be Formed? GMAT Problem Solving
• 4 Bells Toll Together at 9:00 A.M. They Toll After 7, 8, 11 and 12 Seconds GMAT Problem Solving
• 12 Marbles are Selected at Random from a Large Collection of White, Red, Green and Yellow Marbles GMAT Problem Solving
• A welder received an order to make a 1 million litre cube-shaped tank GMAT Problem Solving
• After 6 games, Team B had an average of 61.5 points per game GMAT Problem Solving
• A Man has 1044 Candles. After Burning, He can Make a New Candle GMAT Problem Solving
• If 12 Ounces of a Strong Vinegar Solution are Diluted with 50 Ounces of Water to Form a Three-Percent Vinegar Solution, What was the Concentration of the Original Solution? GMAT Problem Solving
• If k is an Integer and 2 < k < 7, for How Many Different Values of k is There a Triangle With Sides of Lengths 2, 7, and k? GMAT Problem Solving
• Excluding Stoppages, The Speed of a Bus is 54km/hr and Including Stoppage, It is 45km/hr GMAT Problem Solving
• At a Dog Competition, a Dog is Awarded 10 Points if it Runs Through 4 Pipes, Makes 10 Jumps, and Walks on 2 Beams. GMAT Problem Solving
• If m Lies Between The Integers p and s On the Number Line Shown GMAT Problem Solving
• A Cube Of Side 7 cm Is Coloured On Pair of Opposite Faces By Red, Green and Yellow Shades GMAT Problem Solving
• If x^2 − 5x − 6 = 0, which of the following could be x ? GMAT Problem Solving
• How Many Numbers Between 1 and 1000, Inclusive Have an Odd Number of Factors? GMAT Problem Solving
• How Many Factors of 80 are Greater Than\(\sqrt80\)? GMAT Problem Solving
• If \(2^{98}=256L+N\) , Where L and N are Integers and \(0\leq{N}\leq{4}\) , What is the Value of N? GMAT Problem Solving
• Two Dice are Thrown Simultaneously. What is the Probability of Getting Two Numbers Whose Product is Even? GMAT Problem Solving
• The Smallest 3-Digit Positive Integer Obtained By Adding Two Positive Two-Digit Numbers GMAT Problem Solving
• Train A Leaves New York at 9am Eastern Time on Monday, Headed for Los Angeles at a Constant Rate GMAT Problem Solving
• An Express Train Traveled At An Average Speed of 100 Kilometers Per Hour GMAT Problem Solving
• The Hexagon ABCDEF is Regular GMAT Problem Solving
• If x is not equal to zero, and x + 1/x = 3, then what is the value of x^4 + 1/x_4? GMAT Problem Solving
• If mn ≠ 0 and 25 Percent of n Equals 37 1/2 Percent of m, What is the Value of 12n/m? GMAT Problem Solving
• How many multiples of 7 are there between 21 and 343, exclusive? GMAT Problem Solving
• How many odd factors does 210 have? GMAT Problem Solving
• How many three-digit integers are not divisible by 3? GMAT Problem Solving
• How many three-digit numbers are there such that all three digits are different and the first digit is not zero? GMAT Problem Solving
• After 6 Games, Team B Had an Average of 61.5 Points Per Game. GMAT Problem Solving