Crate #1 contains 3 apples, 4 oranges, and 2 pears. Crate #2 contains 5 apples and 3 pears. Julia wants a piece of fruit and to select it she will roll a fair die, selecting a random fruit from Crate #1 if the die shows a 3 or 4 and otherwise selecting it from Crate #2. (a) Find the probability that the selected fruit is a pear. (b) Given that the selected fruit is a pear, find the probability that it came from Crate #1.

Crate #1 contains 3 apples, 4 oranges, and 2 pears. Crate #2 contains 5 apples and 3 pears. Julia wants a piece of fruit and to select it she will roll a fair die, selecting a random fruit from Crate #1 if the die shows a 3 or 4 and otherwise selecting it from Crate #2. (a) Find the probability that the selected fruit is a pear. (b) Given that the selected fruit is a pear, find the probability that it came from Crate #1.

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...

See similar textbooks

Similar questions

Alex decides to go to a casino and play his 3 favorite slot machines. He knows from experience that his chances for coming out ahead and having won money after playing 20 times on a machine is 0.42, 0.55, and0.59 for the three slot machines. Find the probability that after playing each machine 20 times that he will have won money on at least one slot machine. Your answer should be to 4 decimal places.
Whitney wants to practice shooting for basketball. Her mom will give her $20 if she makes 3 free throws in a row, $10 for 2 free throws, and $5 for 1 free throw. Whitney will pay her mom $10 for no free throws. She normally scores 68% of the time. What is the probability that she makes all 3 free throws? What is the probability that she only makes 2 free throws? What is the probability that she only makes 1 free throw? What is the expected value for how much money she can expect to make?
A basketball player makes an average of 2 free throws out of every three attempts. If the player shoots ten free throws, what is the probability that he will make exactly seven shots?
A group of five students went to a hotel with 10 upper floors and a ground floor. The students simultaneously enter the elevator at the ground floor. The students choose their exit floors independently of each other. Determine the probability that they are all going to different floors when each student randomly chooses one of the 10 floors as their exit floor.
A lock consists of 3 dials, where each dial has 4 letters. What is the probability of guessing the right combination in one try? Kay has an 80% probability of making a free-throw in basketball, and each free-throw is independent. Kay gets to take 2 free-throws and must make both to win the game. What is the probability that Kay's team will win the game? Two owners of a cattle ranch, Jo and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows: Jo weighs 25 cows and gets an average weight of 1,350 pounds (stdev 50) Val weighs 100 cows and gets an average weight of 1,420 pounds (stdev 50) What is Jo’s margin of error, rounded to the nearest whole number? (The formula is )
There are 3 bags. The first bag contains 3 red and 7 black balls. The second bag contains 8 red and 2 black balls. The third bag contains 4 red and 6 black balls. One bag is selected randomly and a ball is drawn from it. If the drawn ball is red, the probability that it was drawn from the third bag is
A jar contains 2 red marbles, 8 green marbles, and 5 blue marbles. What is the probability that you draw 3 green marbles in a row if you do replace the marbles after each draw? = What is the probability that you draw 6 blue marbles in a row if you don't replace the marbles after each draw?
In a suitcase there are 5 orange, y green, (y+2) grey and 6 yellow pens. Probability of choosing one green pen from the given suitcase is 1/3. What is the sum of the number of green, grey and yellow pens?