1. Let \( X \) be a continuous random variable whose probability density function is \[ f(x)=\left\{\begin{array}{ll}\frac{x^{3}}{4} & 0 \leq x \leq c \\ 0 & \text { otherwise }\end{array}\right. \] What is the value of \( c \) that makes \( f(x) \) a valid probability density function (PDF).

Em uma urna estão 10 bolas azuis e 6 amarelas. Qual a probabilidade de retirar uma bola amarela desta urna?

Tres monedas cuyas caras son aquila y sol respactiva mente se lanza al aite al mismo ticmpo

D. 300 15. En una bolsa hay varias docenas de caramelos de 4 sabores distintos. El número mínimo de caramelos que deben extraerse de la bolsa, sin mirar su contenido, para tener la seguridad de haber sacado 5 del mismo sabor es: A. 10 B. 13 C. 17 D. 19

Use the following probabilities to answer the question. It may be helpful to sketch a Venn diagram. \( P(A)=0.45, P(B)=0.45 \) and \( P(A \operatorname{and} B)=0.10 \). \( P(\operatorname{not} B \mid A)=\square \) Question Help: \( \square \) Video

Determine the probability that: 1.1 the team will win both matches? 1.2 the team loses both matches? 1.3 the team wins exactly one match? 1.4 the team wins at least one match? 1.5 the team loses the first match but wins the second?