There are 20 buttons in a bag: 8 white buttons, 2 orange buttons, and 10 brown buttons. If one of these buttons is selected at random, what is the probability of selecting either a white or brown button?

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).

(b) If an output component is only accepted when its length lies in the range between 112.8 mm and 168.0 mm , find the expected proportion of components that are accepted i.e. determine the below probability Enter your answer rounded correct to 4 decimal places \( P(112.8<X<168.0)= \) Number (7.5 Mark) Click on Verity to continue Section Attempl 1 of 1

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 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

The PMF of a random varlable \( X \) taking value in \( N \cup\{0\} \) is given by \( P_{I}(i)=e^{-\lambda} \frac{\lambda^{i}}{n}, i=0,1,2, \ldots \) where \( \lambda \) is a positive real number. Given that \( \lambda=2 \), find \( P(X=0) \) \( P(X>2) \)