9. A bowl contains 10 blue balls and 10 green balls. A girl selects balls at random without Iooking atthem.(i)How many balls must she select to be sure of having at least three balls of the samecolour?(ii)How many balls must she select to be sure of having at least three green balls?

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Answered: 9. A bowl contains 10 blue balls and 10…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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At the National Baseball Batting Contest, the organizers have set up game booths for the contestants. Richard wants to win a large stuffed animal. The rules of the game are as follows: You are pitched 5 fastballs, and you must hit them into a fair zone to count. • If you successfully hit all 5 pitches, you win a large stuffed animal. If you successfully hit 3 or 4 pitches, you win a small stuffed animal. • If you successfully hit 1 or 2 pitches, you win a bat-shaped pencil. If you miss all the pitches, you do not win a prize. • The game costs $3 to play (each set of 5 fastballs). Everyone has the same chance as Richard to win. If 160 people each play the game once, how many large stuffed animals will be won?
COUNTING TECHNIQUES - Statistics and probability 1). Maria is organizing her bachelorette party with 18 colleagues from work and 15 from the university. If Maria can only invite 16 of which at least 14 of them must be coworkers In how many ways can she invite her Mary to her companions?
A teacher has two large containers filled with blue, red, and green beads, and claims the proportion of red beads is the same in each container. The students believe the proportions are different. Each student shakes the first container, selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container. One student’s samples contained 10 red beads from the first container and 16 red beads from the second container. Let p1 = the true proportion of red beads in container 1 and p2 = the true proportion of red beads in container 2. Which of the following are the correct hypotheses to test the students’ claim?
A product shipment contains 6 computer chips, of which two (2) are defective. If an inspector selects 4 chips at random for an order, without replacement, how many ways are there of picking both defective chips in this order (of 4 chips)? Order does not matter.
(a) A company has 31 salespeople. A board member at the company asks for a list of the top 4 salespeople, ranked in order of effectiveness. How many such rankings are possible? (b) From the 13 albums released by a musician, the recording company wishes to release 10 in a boxed set. How many different boxed sets are possible
3. Three dice is thrown. a. How many different outcomes are possible? b. If you picked a certain sum as your lucky number, in how many ways could you get a sum of: b₁ : b₂ : b3 : b4 : bs : 4 3 17 18 20
A: Green is just as likely as red or blue to appear. B: Green is just as likely as blue to appear, but not as likely as red. C: Green is not as likely as red or blue to appear. D: Green is not as likely as blue to appear, but is as likely as red.
PigeonHole principle A drawer holds a dozen brown socks and a dozen black socks, both of which are unmatched. In the dark, a man pulls socks at random. a) How many socks does he need to remove to ensure that he has at least two socks of the same color? b) How many socks does he need to pull out to ensure he has at least two black socks?
In a class there are 4 students who are 19 years old and obtained 80 pints in the midterm. There are 6 students who are 19 years old and obtained 50 pints in the midterm. There are 6 students who are 20 years old and obtained 80 pints in the midterm. There are n students who are 20 years old and obtained 50 pints in the midterm. There are no other students. We randomly pick a student in the class, let their age be X and their score by Y. If we are given that X, Y are independent random variables, then compute n.
how many are the possible cases, regardless of the order, for the toss of a coin n times?
15) Use the situation below to answer the question that follows. Team Jet has 7 members who won a school competition. Of these 7, 4 members are randomly picked to receive prizes for winning. The 1st member selected wins a $50 gift card; the 2nd person selected wins a $25 gift card; the 3rd person selected wins a $10 gift card; the 4th person selected wins a $5 gift card. The names of Team Jet's members are represented by the first letter of their first names, as displayed in the following table: Name Frank Gina Harriet Inez Jakob Keven Liu Letter F G H I J K L In the box below, complete the remaining three rows of the list that models how to calculate the number of possible ways 4 team members can be selected to win the prizes. 1) FGHIJKL Let Lui win the 1st prize, so select L. 2) 3) 4)
A father and his three children decide to hold a vote to select an after dinner activity. They will either see a play or a movie. If the majority of the family agrees on a preferred activity, then they will do that activity. If two family members vote to see a play and the other two family members vote to watch a movie, then (since the father will pay for the activity), the father's vote will be used to break the tie. (a) How many winning coalitions are there in this situation? (b) Find one of the children's Banzhaf power index.

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9. A bowl contains 10 blue balls and 10 green balls. A girl selects balls at random without looking at them. (i) How many balls must she select to be sure of having at least three balls of the same colour? (ii) How many balls must she select to be sure of having at least three green balls?