Question: A certain basket contains 10 apples, 7 of which are red and 3 are green. If 3 different apples are randomly selected, what is the probability that out of those 3, 2 will be red and 1 will be green ?
- 7/40
- 7/20
- 49/100
- 21/40
- 7/10
Correct Answer: D
Solution and Explanation:
Approach Solution 1:
The problem statement informs that:
Given:
- A certain basket contains 10 apples, 7 of which are red and 3 are green.
- 3 different apples are randomly selected.
Find Out:
- The probability that out of those 3, 2 will be red and 1 will be green.
The number of ways to select 2 different red apples out of 7 is \(C_7^2={(7*2)\over2!} =21\)
The number of ways to choose 1 green apple out of \(3=C_3^1=3\)
The total number of ways to choose 3 different apples out of total 10 apples \(= C_{10}^3={(10*9*8)\over3*2}\)
= 5*3*8 = 120
As per the formula of Probability, we know that:
Probability = Number of favorable outcomes / total number of outcomes;
Hence, \(P = {C_7^2*C_3^1\over{C_{10}^3}}= {21 * 3\over120} = {63\over120} = {21\over40}\)
Therefore, the probability that out of those 3, 2 will be red and 1 will be green = \(21\over40\)
Approach Solution 2:
The problem statement states that:
Given:
- A certain basket contains 10 apples, 7 of which are red and 3 are green.
- 3 different apples are randomly selected.
Find Out:
- The probability that out of those 3, 2 will be red and 1 will be green.
We can solve the problem by using the probability approach.
That is we can say:
\(P(RRG)= {3!\over{2!}} * {7 \over10} * {6\over9} * {3\over8}={21\over40}\)
Here, we are multiplying by 3!/2! as the case of RRG can occur in 3 ways: RRG, RGR, GRR - the number of permutation of 3 letters out of which 2 are identical.
Therefore, the probability that out of those 3, 2 will be red and 1 will be green =\(21\over40\).
Approach Solution 3:
The problem statement states that:
Given:
- A certain basket contains 10 apples, 7 of which are red and 3 are green.
- 3 different apples are randomly selected.
Find Out:
- The probability that out of those 3, 2 will be red and 1 will be green.
We can solve the problem by applying certain rules of probability.
Let's find the probability of choosing a red apple 1st, a red apple 2nd, and a green apple 3rd (i.e RRG)
P(red apple 1st AND red apple 2nd AND green apple 3rd) = P(red apple 1st) x P(red apple 2nd) x P(green apple 3rd)
= 7/10 x 6/9 x 3/8
= 7/40
It is important to select a red apple 1st, a red apple 2nd, and a green apple 3rd (i.e RRG). It is just ONE WAY to get 2 red apples and 1 green apple. There are also other ways like RGR and GGR.
We already know that P(RRG) = 7/40, which implies that P(RGR) = 7/40 and P(GRR) = 7/40
Therefore, P(select 2 red apples and 1 green apple) = P(RRG or RGR or GRR)
= P(RRG) + P(RGR) + P(GRR)
= 7/40 + 7/40 + 7/40
= 21/40
Thus, the probability that out of those 3, 2 will be red and 1 will be green is = 21/40.
“A certain basket contains 10 apples, 7 of which are red and 3 are green” - is a topic of the GMAT Quantitative reasoning section of the GMAT exam. This topic has been taken from the book “GMAT Official Guide 2021”. To solve the GMAT Problem Solving questions, the candidates must gain concrete knowledge of mathematics and calculations. The GMAT Quant practice papers further help the candidates to analyse varieties of questions that will enable them to improve their mathematical knowledge.
Suggested GMAT Problem Solving Questions
- Paul, Quallis and Robert Divide a Sum of Money Among Themselves in the GMAT Problem Solving
- If A Sphere With Radius r Is Inscribed In A Cube With Edges Of Length GMAT Problem Solving
- A Globe Of Radius 8 Inches Is To Be Placed Into A Square Box For Shipment GMAT Problem Solving
- What is the sum of digits in decimal notation of number (10^20) - 16? GMAT Problem Solving
- Which of the following is equivalent to the pair of GMAT Problem Solving
- A password to a certain database consists of digits that can GMAT Problem Solving
- A Can do 1/3 of the Work in 5 Days and B Can do 2/5 of the Work in 10 Days GMAT Problem Solving
- The income of a broker remains unchanged though the rate of commission is increased GMAT Problem Solving
- Curly Brackets {} Around the Last Digits of a Decimal Fraction Signify GMAT Problem Solving
- For the infinite sequence a1, a2, a3, ... an, an+1, an=3(an−1) for all GMAT Problem Solving
- The quantities S and T are positive and are related by the equation GMAT Problem Solving
- A child paints the six faces of a cube with six different GMAT Problem Solving
- In an opera theater. there are 300 seats available GMAT Problem Solving
- At the Rate of m Meters Per s Seconds, How Many Meters Does a Cyclist GMAT Problem Solving
- NASA Received Three Messages in a Strange Language From a Distant Planet GMAT Problem Solving
- Two Cyclists Start From the Same Place to Ride in the Same Direction GMAT Problem Solving
- A Sphere is Inscribed in a Cube with an Edge of 10. What is GMAT Problem Solving
- If AC = BC and CD = DE Then, in Terms of x, the Value of y is GMAT Problem Solving
- What Is The Units Digit Of The Product Of Any Five Consecutive Positive Integers GMAT Problem Solving
- A Large Cube Consists Of 125 Identical Small Cubes GMAT Problem Solving
- A Pizzeria Makes Pizzas That Are Shaped As Perfect Circles GMAT Problem Solving
- The Number Of Diagonals Of A Polygon Of n Sides Is Given By The Formula GMAT Problem Solving
- The Work Done By A Woman In 8 Hours Is Equal To The Work Done By A Man GMAT Problem Solving
- A Circle Is Inscribed Inside Right Triangle Abc Shown Above GMAT Problem Solving
- The Temperatures In Degrees Celsius Recorded At 6 In The Morning In GMAT Problem Solving
- A Truck Travelling At 70 Kilometres Per Hour Uses 30% More Diesel To GMAT Problem Solving
- If The Area Of A Rectangle Is Equal To The Area Of A Square, Then The GMAT Problem Solving
- The rectangles shown above are similar and the ratio of the area of GMAT Problem Solving
- A School has Set Different Minimum Qualifying Marks in an Exam GMAT Problem Solving
- The Temperature of Delhi and Lucknow were in the Ratio 3:5 in July GMAT Problem Solving
- When a Certain Tree was First Planted, it was 4 feet Tall and the Height GMAT Problem Solving
- When a Number A is Divided by 6, the Remainder is 3 and When Another GMAT Problem Solving
- Which of the Following is the Correct Ordering of 2√13, 4√3, 5√2 and 3√6 ? GMAT Problem Solving
- If the mean of set S does not exceed mean of the subset of set S, which GMAT Problem Solving
- A Milkman Sells Milk after Adding Some Water in it GMAT Problem Solving
- It Was Observed by National Geographic that Equinox Happened GMAT Problem Solving
- Paracelsus University has Two Kinds of Professors, Academic Professors GMAT Problem Solving
- What is the Smallest Prime Factor of 5^8+10^6–50^3? GMAT Problem Solving
- In A Locality, There Are Ten Houses In A Row. On A Particular Night GMAT Problem Solving
- The “Connection” Between Any Two Positive Integers a And b GMAT Problem Solving
- Find the least positive integers which must be added to 15,463 so that the result GMAT Problem Solving
- Mayank Buys Some Candies for $15 a dozen and An Equal Number of Different GMAT Problem Solving
- If John Throws a Coin Until a Series of Three Consecutive Heads GMAT Problem Solving
- In the Diagram Above, ABCD is a Parallelogram and the Areas of Yellow GMAT Problem Solving
- On certain road 10% of the motorists exceed the posted speed limit GMAT Problem Solving
- If n is a positive integer and the product of all the integers from 1 to n GMAT Problem Solving
- John has 10 pairs of matched socks. If he loses 7 individual socks GMAT Problem Solving
- If x is an integer and 4^x < 100, what is x? GMAT Problem Solving
- The ratio 2 to 1/3 is equal to the ratio GMAT Problem Solving
- In the Decimal Notation of Number (2/23)^3. What is the Third Digit GMAT Problem Solving
Comments