Calcolo Combinatorio e Probabilità: 4 Quesiti Maturità

We'll cover all the combinatorics and probability questions from the 2023, 2024, and 2025 final exams, explaining everything step by step! 0:00 - Exercise 1 6:49 - Exercise 2 20:45 - Exercise 3 27:00 - Exercise 4 Useful links: Maturity exam playlist:    • Maturità - Ripasso Matematica (Licei Scien...   Derivatives of composite functions:    • 15 Esercizi Svolti sulle Derivate di Funzi...   If you need private online lessons or would like more information, please email me at: [email protected] Texts: 1) A loaded die, with faces numbered 1 through 6, has the property that each even face is twice as likely to appear as each odd face. Calculate the probability of rolling the die once, respectively, of obtaining: a prime number; a number at least equal to 3; a number at most equal to 3. 2) A biased coin is tossed 5 times, landing heads with probability p. What is the probability of landing heads exactly twice? For what value of p is the probability of landing heads exactly twice greatest? 3) Cicero, in his dialogue with his brother Quintus, discusses the Venus flip, which consists of rolling four four-sided dice and obtaining four different results. Assuming that the faces of each die are equally probable, determine: the probability of obtaining the Venus flip in rolling four dice; the probability of rolling four identical numbers. 4) How many anagrams, even meaningless, are there for the word "STUDIARE"? How many of these anagrams can be read consecutively for the word "ARTE," such as "SUARTEDI"? How many anagrams, even meaningless, are there for the word "VACANZA"?