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) $\frac { 1 } { 9 }$

In the Venn diagram below

• Set A represents integers divisible by 2 without remainder,
• Set B represents integers divisible by 3 without remainder,
• Set C represents integers divisible by 12 without remainder.

Accordingly,
I. 18
II. 24
III. 42
Which of these numbers is an element of the set represented by the shaded region?
A) Only I
B) Only II
C) I and II

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) $\frac { 3 } { 16 }$

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

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

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) $\{ 4,5,7,8,9 \}$

An exam consisting of a total of 8 questions, with 4 questions each in the verbal and quantitative sections, has the following statement in its booklet: ``To pass the exam, you must answer at least 5 questions correctly in total, with at least 2 questions from each of the verbal and quantitative sections.'' Sevcan, who read this statement incompletely, randomly selected 5 out of 8 questions on the exam and answered each question she selected correctly.
Accordingly, what is the probability that Sevcan passes the exam?
A) $\frac{3}{4}$
B) $\frac{4}{5}$
C) $\frac{5}{6}$
D) $\frac{6}{7}$
E) $\frac{7}{8}$

Kerem randomly selects 3 numbers using the buttons shown in the figure to create the password for his locker, such that each is in a different row and different column.
Accordingly, what is the probability that all of the numbers Kerem selected are odd?
A) $\frac{1}{2}$
B) $\frac{1}{3}$
C) (from figure)
D) $\frac{5}{9}$
E) $\frac{4}{27}$

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) $\frac{1}{6}$

Aras divides all of his marbles into groups of 3 and obtains a two-digit natural number AB, and divides them into groups of 8 and obtains a two-digit natural number BA.
According to this, if Aras divides all the marbles he has into groups such that each group has an equal number of marbles, which of the following could be the number of groups he obtains?
A) 40 B) 48 C) 54 D) 56 E) 60

A stove consisting of 1 large, 2 medium, and 1 small compartment with 4 ignition buttons, each of which activates a different compartment, is shown in the figure below.
Since the directions next to the buttons have been erased, it is not known which button activates which compartment.
Accordingly, when all compartments are closed and two buttons are randomly pressed, what is the probability that one of the medium compartments and the small compartment will activate?
A) $\frac{1}{2}$ B) $\frac{1}{3}$ C) $\frac{2}{3}$ D) $\frac{1}{4}$ E) $\frac{1}{5}$

A certain bus arrives at the bus stop near Duru's house with probability $\dfrac{7}{10}$ at exactly 09:02 and with probability $\dfrac{3}{10}$ at exactly 09:03. Duru leaves home at exactly 09:00 to catch this bus. The time it takes for Duru to reach the stop is 100 seconds with probability $\dfrac{1}{2}$, 150 seconds with probability $\dfrac{3}{10}$, and 250 seconds with probability $\dfrac{1}{5}$.
What is the probability that Duru is at the stop when the bus arrives?
A) $\dfrac{55}{100}$ B) $\dfrac{59}{100}$ C) $\dfrac{63}{100}$ D) $\dfrac{67}{100}$ E) $\dfrac{71}{100}$

Six friends, including Doğa and Duru, came to visit Defne's house. Defne randomly gave gifts to two of these friends.
According to this, what is the probability that Defne gave a gift to at least one of Doğa and Duru?
A) $\frac{2}{3}$ B) $\frac{3}{5}$ C) $\frac{4}{5}$ D) $\frac{8}{15}$ E) $\frac{11}{15}$