a. Find the sample space using a tree diagram to show the possibilities Elaine has to choose a mattress. b. What is the probability that Elaine chooses a memory foam-topped mattress? Write the number of ways Elaine chooses a memory foam-topped mattress. (Refer to sample space) The Sleep Number bed is mattress that adjusts to different levels of softness. After deciding thatshe definitely wants one, Elaine has a few choices to make. These choices are summarized in thetable. She will need to make one choice in each category.SizeTopPillowAdjustmentSleep IQKingQueenMemory foamManualDouble

A sample space is a set that contains all possible outcomes of a particular experiment. To create a sample space, we list down all possibilities for the experiment. Tree diagrams are helpful in determining the sample space as they visually represent all the possible outcomes of the experiment. The probability of an outcome can be calculated by diving the number of favorable outcomes with the total number of outcomes. a. In the given problem, there are three different decisions to make, namely, size, top, and adjustment. To create the tree diagram, we start by different possibilities of size. Then, in the next stage, we include the different possible tops for each possibility of size. In the last stage, we include different possible adjustments for all possibilities of the previous stage. The tree diagram for the experiment can be drawn as follows: In the tree diagram, each branch of the tree represents an outcome. The sample space is the set of all possible outcomes. So, to write the sample space, we list the outcomes of all the branches of the tree diagram. Let's represent the outcome as the tuple s, t, a, where s represents the size, t represents the top, and a represents the adjustment. So, the sample space will be given as follows: S=King, Pillow, Sleep IQ,King, Pillow, Manual,King, Memory foam, Sleep IQ,King, Memory foam, Manual,Queen, Pillow, Sleep IQ,Queen, Pillow, Manual,Queen, Memory foam, Sleep IQ,Queen, Memory foam, Manual,Double, Pillow, Sleep IQ,Double, Pillow, Manual,Double, Memory foam, Sleep IQ,Double, Memory foam, Manual Answer: S={(King, Pillow, Sleep IQ),(King, Pillow, Manual),(King, Memory foam, Sleep IQ),(King, Memory foam, Manual),(Queen, Pillow, Sleep IQ),(Queen, Pillow, Manual),(Queen, Memory foam, Sleep IQ),(Queen, Memory foam, Manual),(Double, Pillow, Sleep IQ),(Double, Pillow, Manual),(Double, Memory foam, Sleep IQ),(Double, Memory foam, Manual)}b. The total number of elements in the sample space is the total possibilities for choosing the mattress. The total number of ways Person E chooses a mattress is 12. Of which 6 ways include choosing the top as Memory foam. Therefore, the required probability is given as follows: P=612=12=0.5 Answer: Probability of choosing memory foam-topped mattress=0.5 Number of ways of choosing memory foam-topped mattress=6

Math

Probability

a. Find the sample space using a tree diagram to show the possibilities Elaine has to choose a mattress. b. What is the probability that Elaine chooses a memory foam-topped mattress? Write the number of ways Elaine chooses a memory foam-topped mattress. (Refer to sample space)

a. Find the sample space using a tree diagram to show the possibilities Elaine has to choose a mattress. b. What is the probability that Elaine chooses a memory foam-topped mattress? Write the number of ways Elaine chooses a memory foam-topped mattress. (Refer to sample space)

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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Question

The Sleep Number bed is mattress that adjusts to different levels of softness. After deciding that
she definitely wants one, Elaine has a few choices to make. These choices are summarized in the
table. She will need to make one choice in each category.
Size
Top
Pillow
Adjustment
Sleep IQ
King
Queen
Memory foam
Manual
Double

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