1 Isabel Briggs Myers was a pioneer in the study of personal

1. Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication.

Suppose that a married couple is selected at random.

(a) Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (Enter your answers to 2 decimal places.)

(b) Do the probabilities add up to 1? Why should they?

Yes, because they do not cover the entire sample space.No, because they do not cover the entire sample space.    Yes, because they cover the entire sample space.No, because they cover the entire sample space.

What is the sample space in this problem?

0, 1, 2, 3 personality preferences in common

1, 2, 3, 4 personality preferences in common    

0, 1, 2, 3, 4, 5 personality preferences in common

0, 1, 2, 3, 4 personality preferences in common

2. M&M plain candies come in various colors. According to the M&M/Mars Department of Consumer Affairs, the distribution of colors for plain M&M candies is as follows.

Suppose you have a large bag of plain M&M candies and you choose one candy at random.

(a) Find P(green candy or blue candy).

Are these outcomes mutually exclusive? Why?

Yes. Choosing a green and blue M&M is not possible.No. Choosing a green and blue M&M is not possible.    No. Choosing a green and blue M&M is possible.Yes. Choosing a green and blue M&M is possible.

(b) Find P(yellow candy or red candy).

Are these outcomes mutually exclusive? Why?

Yes. Choosing a yellow and red M&M is possible.

No. Choosing a yellow and red M&M is not possible.   

Yes. Choosing a yellow and red M&M is not possible

.No. Choosing a yellow and red M&M is possible.

(c) Find P(not purple candy).

3. When do creative people get their best ideas? USA Today did a survey of 966 inventors (who hold U.S. patents) and obtained the following information.

(a) Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a best idea during each time interval: from 6 A.M. to 12 noon, from 12 noon to 6 P.M., from 6 P.M. to 12 midnight, from 12 midnight to 6 A.M. (Enter your answers to 3 decimal places.)

No, because they do not cover the entire sample space.

Yes, because they cover the entire sample space.    

Yes, because they do not cover the entire sample space.

No, because they cover the entire sample space.
(b) Do the probabilities add up to 1? Why should they?

What is the sample space in this problem?

12AM-12PM

6AM-6PM   

6AM-12AM

the entire day

Similarities and Differences in a Random Sample of 375 Married Couples
Number of Similar Preferences	Number of Married Couples
All four Three Two One None	35 122 110 69 39

Solution

1)

A)

P (0) =39 / 375

P (1) =69 / 375=0.18

P (2) = 110 / 375=0.29

P (3) =122/ 375=0.33

P (4) =35 / 375=0.09

(b) Do the probabilities add up to 1? Yes, they do add up to 1

(b) and (c)

Why should they? What is the sample space in this problem?

They should add up to one because the sum of all the probabilities in a sample space add up to1.

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2)

(a) Find P(green candy or blue candy).

P (green candy or blue candy) = P (green) +P (blue) +P (green and blue)

                                                  =0.9 + 0.10 + 0=1

P (green and blue) = 0 because the outcomes are mutually exclusive.

(b) Find P(yellow candy or red candy)

P (yellow candy or red candy) = P (yellow) +P (red) +P (yellow and red)

                                                  =0.18 + 0.17 + 0=0.35

Are these outcomes mutually exclusive? Why?

Yes. Choosing a yellow and red M&M is not possible.

(c) Find P(not purple candy).

P(not purple candy) = 1 - P( purple candy) =1 - 0.20 = 0.8

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3)

(a) Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a best idea during each time interval: from 6 A.M. to 12 noon, from 12 noon to 6 P.M., from 6 P.M. to 12 midnight, from 12 midnight to 6 A.M. (Enter your answers to 3 decimal places.)

P(best idea 6 a.m.