En un juego de apuestas entre los estudiantes de Ingenieria en Minas de la UTH y el profesor de Probabilidad y Estadistica, un estudiante lanza una moneda diez veces. En este juego se tienen en cuenta las siguientes apuestas: a) Si obtiene 5 caras o más, el estudiante obtiene 2 puntos en su examen de la unidad. b) Si obtiene menos de tres caras, no gana ningún punto. c) Si obtiene más de seis caras, el estudiante gana 3 puntos, Calcula las respectivas probabilidades: \( p=0.5 \) \( n=10 \) a) \( P(X \geq 5)= \) b) \( P(X<3)= \) c) \( P(X>6)= \)

here is a spinner with 15 equal areas, numbered 1 through 15 . If the spinner is spun one time, hat is the probability that the result is a multiple of 3 and a multiple of 4 ?

Suppose \( A \) and \( B \) are dependent events. If \( P(A)=0.5 \) and \( P(B \mid A)=0.6 \), what is \( P(A \cap B) \) ? A. 0.5 B. 0.3 C. 0.6 D. 0.1

In a certain Algebra 2 class of 25 students, 15 of them play basketball and 7 of them play baseball. There are 8 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?

What does it mean for two events to be independent in probability?

A basketball player makes \( 70 \% \) of his free throws. If he attempts 20 free throws, what is the probability that he makes at least 15 of them? (Hint: this is a binomial distribution problem with the following parameters: \( n=20 \) as the number of trials and \( p=0.7 \) as the probability of success on a single trial) a. 0.5122 b. 0.3455 c. 0.416 d. 0.1055