Chapter 1: Problem 19
Find the 25 th percentile of the distribution having pdf \(f(x)=|x| / 4\), where
\(-2
Chapter 1: Problem 19
Find the 25 th percentile of the distribution having pdf \(f(x)=|x| / 4\), where
\(-2
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Get started for freeIf \(P\left(A_{1}\right)>0\) and if \(A_{2}, A_{3}, A_{4}, \ldots\) are mutually disjoint sets, show that $$ P\left(A_{2} \cup A_{3} \cup \cdots \mid A_{1}\right)=P\left(A_{2} \mid A_{1}\right)+P\left(A_{3} \mid A_{1}\right)+\cdots $$
There are five red chips and three blue chips in a bowl. The red chips are numbered \(1,2,3,4,5\), respectively, and the blue chips are numbered \(1,2,3\), respectively. If two chips are to be drawn at random and without replacement, find the probability that these chips have either the same number or the same color,
Each bag in a large box contains 25 tulip bulbs. It is known that \(60 \%\) of the bags contain bulbs for 5 red and 20 yellow tulips, while the remaining \(40 \%\) of the bags contain bulbs for 15 red and 10 yellow tulips. A bag is selected at random and a bulb taken at random from this bag is planted. (a) What is the probability that it will be a yellow tulip? (b) Given that it is yellow, what is the conditional probability it comes from a bag that contained 5 red and 20 yellow bulbs?
List all possible arrangements of the four letters \(m, a, r\), and \(y .\) Let \(C_{1}\) be the collection of the arrangements in which \(y\) is in the last position. Let \(C_{2}\) be the collection of the arrangements in which \(m\) is in the first position. Find the union and the intersection of \(C_{1}\) and \(C_{2}\).
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.
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