LFM Stats And Pure

turkey-yks 2012 Q27 Finite Equally-Likely Probability Computation View

Four students of different heights line up randomly in a row.
According to this, what is the probability that the shortest and tallest students are at the ends?
A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 6 }$
E) $\frac { 1 } { 12 }$

turkey-yks 2013 Q22 Optimization of Probability or Strategy View

A bag contains nine balls numbered from 1 to 9. Ayşe will choose a number from 1 to 9 and then draw a ball randomly from the bag. Ayşe wins the game if the sum of the number on the ball and the number she chose is at most 9 and their product is at least 9.
Which number should Ayşe choose so that her probability of winning the game is highest?
A) 2
B) 3
C) 4
D) 5
E) 6

turkey-yks 2014 Q32 Conditional Probability and Bayes' Theorem View

A fair cubic die is rolled and it is known that one of its faces is in contact with the ground.
Given this, what is the probability that only one of the corners A and B is in contact with the ground?
A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 1 } { 6 }$
E) $\frac { 5 } { 6 }$

turkey-yks 2015 Q13 Combinatorial Counting (Non-Probability) View

Let $\mathbf { A } = \{ \mathbf { a } , \mathbf { b } , \mathbf { c } , \mathbf { d } \}$. For non-empty subsets $X , Y$ of A
$$\begin{aligned} & X \cap Y = \emptyset \\ & X \cup Y = A \end{aligned}$$
How many ordered pairs (X, Y) are there such that these conditions hold?
A) 6
B) 8
C) 10
D) 12
E) 14

turkey-yks 2015 Q17 Set Operations View

Below is the graph of a function $f$. $( a > 2 , b < 1 )$
Accordingly, which of the following could be the graph of the function $| \mathbf { f } ( \mathbf { x } + \mathbf { 2 } ) | - \mathbf { 1 }$?
A) [graph A]
B) [graph B]
C) [graph C]
D) [graph D]
E) [graph E]

turkey-yks 2015 Q19 Set Operations View

Let m and n be real numbers. In the expansion of
$$\left( \frac { \mathrm { m } } { \mathrm { nx } } + \frac { \mathrm { nx } ^ { 2 } } { \mathrm {~m} } \right) ^ { 3 }$$
arranged according to powers of x, the constant term is 6.
Accordingly, what is the ratio $\frac { m } { n }$?
A) 1
B) 2
C) 3
D) 4
E) 5

turkey-yks 2015 Q32 Finite Equally-Likely Probability Computation View

Deniz randomly colored two of the following four points that are the vertices of a square red and the other two blue, and drew line segments connecting the points she colored the same color.
What is the probability that these line segments intersect?
A) $\frac { 1 } { 6 }$ B) $\frac { 1 } { 4 }$ C) $\frac { 1 } { 3 }$ D) $\frac { 2 } { 3 }$ E) $\frac { 3 } { 4 }$

turkey-yks 2016 Q17 Set Operations View

Let N be the set of natural numbers. The sets
$$\begin{aligned} & C = \{ 2 n : n \in \mathbb { N } \} \\ & K = \left\{ n ^ { 2 } : n \in \mathbb { N } \right\} \end{aligned}$$
are given. Accordingly, which of the following is an element of the Cartesian product set
$$( \mathrm { K } \backslash \mathrm { C } ) \times ( \mathrm { C } \backslash \mathrm { K } )$$
?
A) $( 3,2 )$
B) $( 9,4 )$
C) $( 15,1 )$
D) $( 16,12 )$
E) $( 25,8 )$

turkey-yks 2016 Q19 Finite Equally-Likely Probability Computation View

In the figure, 3 of the 6 edges of a regular tetrahedron are randomly painted.
Accordingly, what is the probability that all three painted edges are on the same face?
A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 5 }$
E) $\frac { 1 } { 6 }$

turkey-yks 2016 Q33 Finite Equally-Likely Probability Computation View

In a cube, 6 of its 8 vertices are randomly painted white and the other 2 are painted black.
What is the probability that there is an edge with both endpoints painted black in this cube?
A) $\frac { 1 } { 7 }$
B) $\frac { 2 } { 7 }$
C) $\frac { 3 } { 7 }$
D) $\frac { 4 } { 7 }$
E) $\frac { 5 } { 7 }$

turkey-yks 2018 Q16 Finite Equally-Likely Probability Computation View

There is an ant at each of the vertices $K$ and $L$ of a regular tetrahedron.
Each of these ants starts walking along one of the edges emanating from their respective corners, chosen at random, and stops when reaching the other end of that edge.
Accordingly, what is the probability that the ants meet?
A) $\frac { 1 } { 3 }$ B) $\frac { 2 } { 3 }$ C) $\frac { 1 } { 4 }$ D) $\frac { 3 } { 4 }$ E) $\frac { 1 } { 9 }$

turkey-yks 2019 Q20 Finite Equally-Likely Probability Computation View

Ege's bag contains four cards of the same size: an identity card, a student card, a meal card, and a bus card. Ege draws a card randomly from his bag to find the bus card. If he draws the wrong card, he keeps it in his hand and draws another card randomly from his bag, and continues this way until he finds the bus card. What is the probability that Ege finds the bus card on the third attempt?
A) $\frac { 1 } { 4 }$
B) $\frac { 1 } { 8 }$
C) $\frac { 3 } { 8 }$
D) $\frac { 1 } { 16 }$
E) $\frac { 3 } { 16 }$

turkey-yks 2019 Q30 Finite Equally-Likely Probability Computation View

Below are four cards with the numbers 6, 8, 10, and 12 written on them.
Seeing these cards, Yiğit makes the claim:
``If I randomly select two of the cards and add the numbers written on them, the probability that I find my age is $\frac{1}{3}$.''
Given that this claim is correct, what is Yiğit's age?
A) 14
B) 16
C) 18
D) 20
E) 22

turkey-yks 2020 Q8 Set Operations View

Regarding sets $A$, $B$, and $C$
$$\begin{aligned} & \{ ( 1,2 ) , ( 2,3 ) , ( 3,4 ) \} \subseteq A \times B \\ & \{ ( 1,2 ) , ( 3,4 ) , ( 4,2 ) , ( 4,4 ) \} \subseteq A \times C \end{aligned}$$
it is known that.
Accordingly, I. The set $A \cap B$ has at least 3 elements. II. The set $A \cap C$ has at least 3 elements. III. The set $B \cap C$ has at least 3 elements. which of these statements are always true?
A) Only I
B) Only II
C) Only III
D) I and II
E) I and III

turkey-yks 2020 Q9 Set Operations View

If the number of elements of a set whose all elements are positive integers is one more than the value of the smallest element of this set, this set is called a wide set.
Let $A$, $B$, and $C$ be wide sets,

$A \cup B \cup C = \{ 1,2,3,4,5,6,7,8,9 \}$
$A \cap B = \{ 3 \}$
$1 \in A$
$6 \in B$

it is known that. Accordingly, which of the following is set $C$?
A) $\{ 1,2 \}$
B) $\{ 3,4,8,9 \}$
C) $\{ 3,5,7,8 \}$
D) $\{ 4,5,6,7,8 \}$
E) $\{ 4,5,7,8,9 \}$

turkey-yks 2021 Q15 Conditional Probability and Bayes' Theorem View

Two different digits are randomly selected from the set $A = \{ 1,2,3,4,5,6,7 \}$.
Given that the product of the selected digits is an even number, what is the probability that the sum of these digits is also an even number?
A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 5 }$
E) $\frac { 1 } { 6 }$

turkey-yks 2021 Q30 Finite Equally-Likely Probability Computation View

To access an internet site, users must select all unit squares containing car parts from the photograph divided into 9 unit squares below and click the confirm button.
Eda, who wants to access this site, randomly selected four different unit squares from this photograph and clicked the confirm button.
Accordingly, what is the probability that Eda can access this site?
A) $\frac{1}{15}$ B) $\frac{1}{36}$ C) $\frac{1}{56}$ D) $\frac{1}{84}$ E) $\frac{1}{126}$

turkey-yks 2023 Q7 Combinatorial Counting (Non-Probability) View

The figure below shows a lamp and the appearance of a string that operates this lamp. The lamp;

when closed, if the string is pulled and released, it gives dim light,
when giving dim light, if the string is pulled and released, it gives daylight,
when giving daylight, if the string is pulled and released, it gives bright light,
when giving bright light, if the string is pulled and released, it turns off.

Initially, this lamp was closed. The string was pulled and released A times and the lamp was observed to give bright light. Then, the lamp's string was pulled and released B more times and the lamp was observed to give daylight. Later, the lamp's string was pulled and released C more times and the lamp was observed to turn off.
Accordingly, which of the following is an even number?
A) $A \cdot B + C$ B) $B \cdot C + A$ C) $A \cdot (B + C)$ D) $B \cdot (A + C)$ E) $C \cdot (A + B)$

turkey-yks 2023 Q9 Combinatorial Counting (Non-Probability) View

At the entrance of a hotel, there are three digital wall clocks showing the local times of cities $\mathrm{A}, \mathrm{B}$ and C. A customer looking at these clocks observed that the local time difference between cities A and B is 4 hours, and the local time difference between cities B and C is 3 hours.
When the clock showing the local time of city A reads 14.00, which of the following cannot be the time shown on the clock for city C?
A) 07.00 B) 13.00 C) 15.00 D) 17.00 E) 21.00

turkey-yks 2023 Q11 Finite Equally-Likely Probability Computation View

Before the doctor's examination, Sibel Hanım's age, height, and weight are written on a card.

Age : 53

Height : .......

Weight : .......

Regarding this information,
$p$: Sibel Hanım's weight is more than 60 kilograms.
$q$: Sibel Hanım's height is in the range of 164 cm to 170 cm.
$r$: Sibel Hanım's age is in the range of 55 to 65.
propositions are given.
$$\left( p \Rightarrow q^{\prime} \right) \wedge r^{\prime}$$
Given that this proposition is false, which of the following could be Sibel Hanım's height and weight?
A) $160 \mathrm{~cm} - 56$ kilograms B) $165 \mathrm{~cm} - 58$ kilograms C) $166 \mathrm{~cm} - 62$ kilograms D) $171 \mathrm{~cm} - 59$ kilograms E) $172 \mathrm{~cm} - 64$ kilograms

turkey-yks 2023 Q13 Combinatorial Counting (Non-Probability) View

The number of different digits in a natural number N is defined as shown in the figure.
Example: $4202 = 3$
Let A be a digit, and the equality shown in the figure holds.
What is the sum of different A values that satisfy the equality?
A) 8 B) 9 C) 10 D) 11 E) 12

turkey-yks 2023 Q14 Combinatorial Counting (Non-Probability) View

Among the three-digit natural numbers $ABB$ and $BAB$, one is divisible by 11 and the other is divisible by 12.
Accordingly, what is the sum $\mathrm{A} + \mathrm{B}$?
A) 7 B) 8 C) 10 D) 11 E) 13

turkey-yks 2023 Q14 Finite Equally-Likely Probability Computation View

Veysel has four gift vouchers of 200, 400, 600 and 800 TL from a clothing store. Veysel randomly gives one of these four gift vouchers to each of his two daughters, Yasemin and Zehra, who want to shop at this clothing store. On different days, Yasemin likes a dress for 300 TL and Zehra likes a dress for 500 TL.
Accordingly, what is the probability that both girls can buy the dresses they like with only the gift vouchers they received from their father?
A) $\frac{1}{2}$ B) $\frac{1}{3}$ C) $\frac{1}{4}$ D) $\frac{1}{5}$ E) $\frac{1}{6}$

turkey-yks 2023 Q15 Combinatorial Counting (Non-Probability) View

Let $A, B$ and $C$ be digits different from zero and from each other; the sum of the two-digit natural number AB and the two-digit natural number BC equals one less than the two-digit natural number CA.
Accordingly, how many different three-digit natural numbers ABC can be written using the digits A, B, and C that satisfy this condition?
A) 1 B) 2 C) 3 D) 5 E) 6

turkey-yks 2023 Q18 Combinatorial Counting (Non-Probability) View

Boat trips are organized for visitors who want to visit a tourist island. The boat departs when there are at least 20 passengers and can carry a maximum of 35 passengers. On a particular day, 3 boat trips were organized and a total of 91 passengers were transported. The ratio of the number of passengers transported in the first trip to the number of passengers transported in the second trip is $\frac{4}{5}$.
Accordingly, how many passengers were transported in the third trip?
A) 21 B) 24 C) 28 D) 32 E) 35

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LFM Stats And Pure

Completing the square and sketching 61

Inequalities 181

Discriminant and conditions for roots 65

Solving quadratics and applications 131

Curve Sketching 228

Factor & Remainder Theorem 61

Polynomial Division & Manipulation 35

Binomial Theorem (positive integer n) 197

Function Transformations 28

Composite & Inverse Functions 211

Partial Fractions 12

Generalised Binomial Theorem 10

Complex Numbers Arithmetic 207

Complex Numbers Argand & Loci 159

Permutations & Arrangements 255

Combinations & Selection 237

Measures of Location and Spread 181

Probability Definitions 212

Tree Diagrams 18

Principle of Inclusion/Exclusion 33

Independent Events 35

Conditional Probability 167

Discrete Probability Distributions 176

Uniform Distribution 3

Binomial Distribution 101

Geometric Distribution 8

Hypergeometric Distribution 9

Negative Binomial Distribution 1

Modelling and Hypothesis Testing 22

Hypothesis test of binomial distributions 2

Data representation 21

Continuous Probability Distributions and Random Variables 322

Continuous Uniform Random Variables 3

Geometric Probability 16

Normal Distribution 87

Approximating Binomial to Normal Distribution 4

Sign Change & Interval Methods 26

Fixed Point Iteration 9

Newton-Raphson method 6