A pack of 12 cards contains either red or black cards. What is the probability that a card chosen at random will be a red card?
(1) The pack has 6 more red cards than black cards
(2) The pack has 3 red cards for every black card
Steps 1 & 2: Understand Question and Draw Inferences
Given: A pack of 12 cards – Black or Red
To find: P(Choosing a Red card)
Step 3: Analyze Statement 1 independently
Statement 1 says that ‘The pack has 6 more red cards than black cards
Thus, Statement 1 alone is sufficient to provide a unique value of R
Step 4: Analyze Statement 2 independently
Statement 2 says that ‘The pack has 3 red cards for every black card’
Thus, Statement 2 alone is sufficient to provide a unique value of R
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already got a unique answer in each of Steps 3 and 4, this step is not required
Answer: Option D
Micky and Kevin go to a market to buy fruits. The probability of Micky buying an apple is 0.25 and of Kevin buying an apple is 0.4. Both Micky and Kevin have a 60% chance of eating the fruits they buy. What is the probability that Kevin eats an apple and Micky does not eat an apple?
Given
To Find:P(Kevin eating an apple AND Micky not eating an apple)
Approach
Working Out
What is the probability that when the letters of the word SERENDIPITY are randomly rearranged, the first alphabet of the resulting word is neither T nor E?
Given:
To find: The probability that when the letters of the word are randomly arranged, the first alphabet is not T or E
Approach:
Working Out:
In a classroom, 40% of the boys had read a particular book. What was the probability that a student who was randomly selected from the classroom was a girl who had read the book?
(1) Threeeighths of all students in the classroom had read the book
(2) 20 girls in the classroom had not read the book
teps 1 & 2: Understand Question and Draw Inferences
Given:
To find: P(Choosing a girl has read the book)
Step 3: Analyze Statement 1 independently
Statement 1 says that ‘Threeeighths of all students in the classroom had read the book’
Therefore,
Step 4: Analyze Statement 2 independently
Statement 2 says that ‘20 girls in the classroom had not read the book’
Step 5: Analyze Both Statements Together (if needed)
Combining the 2 statements, we can write:
Answer: Option E
A playgroup is made up entirely of n pairs of siblings, including the siblings Adam and Josh. 4 members of the playgroup are chosen to represent it in a competition. What is the value of n?
(1) The probability that Adam and Josh are among the 4 members chosen to represent the playgroup is 2/5
(2) The probability that 2 sibling pairs are chosen to represent the playgroup is 1/5
Steps 1 & 2: Understand Question and Draw Inferences
Given:
_{}To find: n = ?
Step 3: Analyze Statement 1 independently
Calculating the Probability that the favorable event will happen
⇒n=3 (rejecting the negative value since number of people cannot be negative)
Thus, Statement 1 alone is sufficient to arrive at a unique value of n.
Step 4: Analyze Statement 2 independently
⇒n=3
(rejecting the negative value since number of people cannot be negative)
Thus, Statement 2 alone is sufficient to arrive at a unique value of n.
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in each of Steps 3 and 4, this step is not required
Answer: Option D
If the probability that Brendon, Daniel and Kane score more than or equal to 700 on the GMAT is 0.4, 0.5 and 0.6 respectively, what is the probability that at least 2 of them score less than 700?
Given
To Find: Probability that atleast 2 of them score less than 700?
Approach
Working Out
A teacher prepares 20 chits, each chit having a unique integer out of the first 20 positive integers. A student is asked to draw a chit at random. What is the probability that the chit drawn by the student does not have a prime number?
Given: 20 chits – each having a unique integer from 1 to 20
To find: P(Choosing a nonprime number)
Approach:
2. P(Choosing a prime number) =
3. So, to answer the question, we will determine the number of prime numbers between 1 and 20
Working Out:
The probability that it rains on a certain day in a week is 0.3. What is the probability that it rains on exactly two days in that week?
Angelo studied the report by an analyst that predicted the probabilities of the returns four stocks may generate in the next one year. Based on the probabilities of the returns, Angelo invested $100 each in four stocks for a year. He plans to sell a stock at the end of the year if the stock is valued at not less than $140. What is the probability that Angelo sells at least 1 of the stocks?
Given
To Find: Probability that atleast 1 of the stock is sold?
Approach
Working Out
Answer: C
A group of 30 people includes men, women and children. If one person is to be chosen at random from the group, is the probability that a man is chosen greater than the probability that a woman is chosen?
(1) The probability that a man is chosen is 50% greater than the probability that a child is chosen.
(2) The probability that either a woman or a child is chosen is greater than the probability that a man is chosen
Steps 1 & 2: Understand Question and Draw Inferences
Given:
To find: Is P(Choosing a man) > P(Choosing a woman)?
Step 3: Analyze Statement 1 independently
Thus, we see that Statement 1 alone is not sufficient to arrive at a unique answer
Step 4: Analyze Statement 2 independently
So, Statement 2 is not sufficient to find a unique answer to the question.
Step 5: Analyze Both Statements Together (if needed)
From Statement 1:
Therefore, even after combining both the statements, we don’t’ know if the answer to the question is Yes or No.
Answer: Option E
If x is an integer such that what is the probability that
Given
To Find: The probability that x^{2 } 2x 8 =0 ?
We need to find the probability that x = 2, or 4
Approach
2. Possible number of values that x can takeà For finding the values that x can take, we need to solve the inequality
3. Probability of
4. For solving the inequality, we will use the wavy line method
Woking Out
1.
James, Kara and Smith are three friends who have applied for a job at Company X. Their probabilities of getting selected for interview are 2/5,1/3and4/7 respectively. If Company X offers a job to only 25% of the applicants it interviews, what is the probability that only Kara receives a job offer out of the three friends?
Given:
To find: Probability that only Kara receives a job offer
Approach:
Working Out:
P(Only Kara receives a job offer) =
Looking at the answer choices, we see that the correct answer is Option B
The probability of a manufacturing company producing a defective item is 0.1. If 5 items are drawn at random from a set of 100 distinct items, what is the probability that at least 2 items would be defective?
Given
To Find: Probability that atleast 2 items will be defective
Approach
Working Out
A box contains balls of two sizes – big and small – and different colors. When one ball is chosen at random from the box, the probability that the ball is blue is 14
. What is the probability that the chosen ball is neither blue nor small?
(1) The probability that the chosen ball is not small is 5/8
(2) The probability that the chosen ball is small but not blue is 9/40
Steps 1 & 2: Understand Question and Draw Inferences
Given:
To find: The probability of choosing a ball that is neither blue nor small
Step 3: Analyze Statement 1 independently
As is clear from the table, we’ve not been able to determine the value of X. So, Statement 1 is not sufficient.
(Note: You may have marked Statement 1 to be sufficient because you thought that:
The catch here, is that Blue and Small are attributes of the same ball. So, these are not independent attributes.
The equation P(Not Small Not Blue) = P(Not Small)*P(Not Blue) would have been correct if the question had stated that there were 2 boxes. In one box, the balls are defined by only their color – they are either blue or not blue. In the second box, they are defined by only their size – small or not small. You have to pick one ball from each box. So, what is the probability that you pick a Not Blue ball from the 1^{st} box and a Not Small box from the 2^{nd} box. This is the scenario where the equation mentioned in this note would be applicable)
Step 4: Analyze Statement 2 independently
This is a linear Equation with only one unknown.
So, it is sufficient to find a unique value of X.
Step 5: Analyze Both Statements Together (if needed)
Since we’ve already arrived at a unique answer in Step 4, this step is not required
Answer: Option B
The first name and the last name of 5 people are written in two tables above, in a jumbled order. For example, the last name of John may be Garth. Lisa, who doesn’t know the correct first namelast name pair for any of the 5 people in the table, is asked to create 5 first name – last name pairs using each first name and last name in the tables above only once. What is the probability that the pairs she creates includes the correct first namelast name pairs of 2 people in the table?
Given:
To find: Probability that 2 out of the 5 FN – LN pairs made by Lisa are correct
Approach:
Working Out:
We are giving the remaining first and last names these generic labels because we do not know exactly which 3 remains are left behind after Task 1.
A mathematics teacher provides the x and y coordinates of 10 points in a rectangular coordinate system. These points are (0.5, 4), (1, 4), (2, 4), (3, 4), (3, 5), (4, 5), (5, 5), (6, 5), (6.5, 5) and (7, 5). He asks a student to select 3 points at random. What is the probability that the chosen points form a triangle?
Given:
To find: P(Chosen points form a triangle)
Approach:
Working Out:
The total number of given points = 10
So, P(Chosen points lie on y = 4) =4/120
Finding P(Chosen points lie on y = 5)
The total number of given points = 10
So, P(Chosen points lie on y = 5) = 20/120
P(Chosen points form a triangle) =
Looking at the answer choices, we see that the correct answer is Option D
The ratio of men to women in a group is 2:3. 36% of the people in the group do not have a college degree while 60% of the women in the group have a college degree. If 1 person is to be randomly selected from the group, what is the probability that he is a man with a college degree?
Given:
This information can be represented visually as follows:
To find: Probability that the chosen person is a Man with a College Degree
Approach:
Working Out:
So, (% of people who are Men with a college degree) = 64%  36% = 28%
Looking at the answer choices, we see that the correct answer is Option D
Frequency Distribution of Integers in Set X and Set Y
X and Y are two sets that contain integers as shown the table above. What is the probability that the product of a randomly chosen integer from Set X and a randomly chosen integer from Set Y will be even?
Given:
To find: The probability that I_{X}*I_{Y} is Even
Approach:
Working Out:
The total number of integers in Set X is 30
Finding the Required Probability
Looking at the answer choices, we see that the correct answer is Option D
In the given figure, ABC is an equilateral triangle such that AD= DB and DF is parallel to EG. If a point is chosen at random inside the triangle, what is the probability that the point would lie inside the quadrilateral DEGF?
Given
To Find: Probability of the point P lies inside the quadrilateral DEFG?
Approach
Working Out
For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. If one integer is selected at random between 5! And 5! + 10, inclusive, what is the probability that the chosen number will have only two factors?
Given:
To find: Probability that the chosen integer will have only 2 factors
Approach:
2.
Working Out:
So, the candidates for primality at this stage are:
{121, 123, 125, 127, 129}
Mary has p pencils and q pens in her bag while Sam has r pencils and s pens in his bag. If Mary and Sam pick up an item at random from their respective bags, who among them has a higher probability of picking up a pencil?
1) p > r
2) q > s
Steps 1 & 2: Understand Question and Draw Inferences
Step 3: Analyze Statement 1 independently
It does not tell us:
Insufficient to answer
Step 4: Analyze Statement 2 independently
2. q > s
It does not tell us:
Insufficient to answer
Step 5: Analyze Both Statements Together (if needed)
Although it gives us the relation between p and r and q and s, it does not tell us how much greater is p than r and q than s.
For example, consider these two cases:
Insufficient to answer
Answer: E
A box contains orange, green and blue balls. If one ball is chosen at random from the box, what is the probability that the chosen ball is orange?
(1) The probability that the chosen ball is blue is onefourth of the probability that the chosen ball is not blue
(2) If there were 15 fewer orange balls in the box, the probability that the chosen ball is orange would have been equal to the probability that the chosen ball is blue
Given:
To find: P(R)
Step 3: Analyze Statement 1 independently
But the expression for the probability that the chosen ball is blue =BR+G+B=
Statement 1 is not sufficient to find a unique answer to the question
Step 4: Analyze Statement 2 independently
Thus, Statement 2 alone is not sufficient to answer the question
Step 5: Analyze Both Statements Together (if needed)
Therefore, the 2 statements together are also not sufficient to answer the question.
Answer: Option E
Two distinct fair dice are rolled together. If a fair coin and a biased coin are also tossed together, what is the probability of getting 1 head and 1 tail on the coins and the sum of the two dice greater than 6? Assume that the probability of getting a head on the biased coin is 0.75.
Given
To Find: Probability of getting 1 head and 1 tail and the sum of the dice > 6
Approach
In the figure above, rectangle PQRS is a shaded region inside the square ABCD. What is the probability that a point chosen at random from the square ABCD will lie inside the shaded rectangle PQRS?
(1) The length of a diagonal of rectangle PQRS is 55% the length of a diagonal of square ABCD
(2) The length of side PQ is 20% greater than the length of side QR
Steps 1 & 2: Understand Question and Draw Inferences
Given: The figure that shows rectangle PQRS inside square ABCD
To find: Probability that a randomly chosen point from the square lies inside the rectangle PQRS
Step 3: Analyze Statement 1 independently
Statement 1 says that ‘The length of a diagonal of rectangle PQRS is 55% the length of a diagonal of square ABCD’
The above equation has 2 unknowns:
Step 4: Analyze Statement 2 independently
Statement 2 says that ‘The length of side PQ is 20% greater than the length of side QR’
However, in order to answer the question, we need to know the value of
Step 5: Analyze Both Statements Together (if needed)
A basket contains red and green balls. If two balls are drawn from the basket without replacement, what is the probability that both balls are red?
(1) If the balls were drawn with replacement, the probability of both balls being red would have been (2/5)^{2}
(2) The ratio of red and green balls in the basket is 2:3
Steps 1 & 2: Understand Question and Draw Inferences
Number of ways to draw 2 balls out of r + g balls =
To Find: Probability of 2 red balls being picked up =
Need to find values of r and g.
Step 3: Analyze Statement 1 independently
(1) If the balls were drawn with replacement, the probability of both balls being red would have been (25)2
Probability of 2 red balls being picked up =
Insufficient to answer the question.
Step 4: Analyze Statement 2 independently
(2) The ratio of red and green balls in the basket is 2:3
Insufficient to answer the question.
Step 5: Analyze Both Statements Together (if needed)
Both the statements give us the same information 3r = 2g.
Insufficient to answer the question.
Answer: E
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