Chapter 1: Problem 5
Let us select five cards at random and without replacement from an ordinary deck of playing cards. (a) Find the pmf of \(X\), the number of hearts in the five cards. (b) Determine \(P(X \leq 1)\).
Chapter 1: Problem 5
Let us select five cards at random and without replacement from an ordinary deck of playing cards. (a) Find the pmf of \(X\), the number of hearts in the five cards. (b) Determine \(P(X \leq 1)\).
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Get started for freeFrom a well shuffled deck of ordinary playing cards, four cards are turned over one at a time without replacement. What is the probability that the spades and red cards alternate?
In a certain factory, machines I, II, and III are all producing springs of the same length. Machines I, II, and III produce \(1 \%, 4 \%\) and \(2 \%\) defective springs, respectively. Of the total production of springs in the factory, Machine I produces \(30 \%\), Machine II produces \(25 \%\), and Machine III produces \(45 \%\). (a) If one spring is selected at random from the total springs produced in a given day, determine the probability that it is defective. (b) Given that the selected spring is defective, find the conditional probability that it was produced by Machine II.
A coin is tossed two independent times, each resulting in a tail (T) or a head (H). The sample space consists of four ordered pairs: TT, TH, HT, HH. Making certain assumptions, compute the probability of each of these ordered pairs. What is the probability of at least one head?
Let \(X\) be the number of gallons of ice cream that is requested at a certain
store on a hot summer day. Assume that \(f(x)=12 x(1000-x)^{2} / 10^{12},
0
Let \(X\) denote a random variable such that \(K(t)=E\left(t^{X}\right)\) exists for all real values of \(t\) in a certain open interval that includes the point \(t=1 .\) Show that \(K^{(m)}(1)\) is equal to the \(m\) th factorial moment \(E[X(X-1) \cdots(X-m+1)] .\)
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