9 Bestimmen Sie die Wahrscheinlichkeit, dass bei fünf Würfen mit einem idealen Würfel \( \begin{array}{ll}\text { a) mindestens eine Sechs fält, } & \text { b) nur gleiche Augenzahlen fallen, } \\ \text { c) die erste Sechs erst im fünften Wurf fällt, } & \text { d) nur im dritten Wurf eine Sechs fallt, } \\ \text { e) genau zwei Sechsen fallen und diese direkt hintereinander. }\end{array} \)

The probability distribution of the discrete random variable \( X \) is \( f(x)=\left(\frac{3}{2}\right)\left(\frac{1}{4}\right)^{x}\left(\frac{3}{4}\right)^{3=x} \) Find the mean of \( X \) (Hint: Give your answerin 2 decimal points).

Dr Faridon Amdjadi, Mechanical Engineering (Tota Find the probability \( P(-1.24<z<-0.07) \) using the standard normal distribution. Select the correct answer. 0.6464 0.6823 0.1841 0.3646

Statistics \& Probability: Two number cubes are thrown one after the other. What is the probability that each number cube shows an even number?

A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with three different members. There are 15 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below. a. How many different ways can the four officers be appointed? There are \( \square \) different ways to appoint the four officers. b. How many different ways can a committee of three be appointed? There are \( \square \) different ways to appoint a committee of three. c. What is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates? P(getting the three youngest of the qualified candidates) = (Type an integer or a simplified fraction.)

Dr Faridon Amdjadi, Mechanical Engineerin Find the probability \( P(-1.15<z<0.09) \) using the standard normal distribution. Select the correct answer. 0.5894