Question

2. Suppose your friend has baked a batch of cookies. Some of them are chocolate chip (C), some are apple flavored (A), and the rest are broccoli flavored (B). Suppose you then took two cookies. Which of the following are sample spaces? If you write that one of these is not a sample space, say why not.

(a) S1 = {AA, AB, AC, BA, BB, BC, CA, CB, CC}, where (e.g.) AB means you got an apple cookie first, and then a broccoli cookie second.

(b) S2 = {0 chocolate chip cookies, 1 chocolate chip cookie, 2 chocolate chip cookies}

(c) S3 = {both cookies are the same flavor, 1 chocolate chip cookie, no chocolate chip cookies}

(d) S4 = {AA, AB, AC, BA, CA, no apple flavored cookies}

(e) S5 = { no chocolate chip cookies, at least one chocolate chip cookie,two chocolate chip cookies}

. Suppose you find 5 random people off the street, and want to find out how many of them have won the lottery in the past.

(a) Write down a sample space that describes the number of lottery winners out of your group of 5.

(b) Are all of the outcomes in y

Answer 1

2)a) S1 contains all the possible samples. We can verify it also.

Total no. of outcomes possible = 3*3=9 ......... (since first cookie can be of any flavor and same for the second cookie )

And counting the no. of outcomes in S1 is also 9.

b)S2 = {0 chocolate chip cookies, 1 chocolate chip cookie, 2 chocolate chip cookies}

0 chocolate chip cookies includes AA , AB, BA, BB

  1 chocolate chip cookie includes AC, CA, BC, CB

  2 chocolate chip cookies Iincludes CC.

So S2=S1 and thus contains all the samples possible

c) S3 = {both cookies are the same flavor, 1 chocolate chip cookie, no chocolate chip cookies}

  both cookies are the same flavor includes AA , BB , CC

  1 chocolate chip cookie includes AC, CA, BC, CB

  no chocolate chip cookies includes AA , AB, BB, BA

so , S3 contains AA and BB twice ,they are considered only once. Thus S3 contains all the samples possible .

d) S4 = {AA, AB, AC, BA, CA, no apple flavored cookies}

No apple flavored cookies includes = BC, BB, CC, CB

thus S4 contains all the possible samples.

e)   S5 = { no chocolate chip cookies, at least one chocolate chip cookie,two chocolate chip cookies}

  no chocolate chip cookies includes AB, BA, AA, BB

at least one chocolate chip cookie includes AC,CA,BC,CB,CC

  two chocolate chip cookies includes CC

taking CC only once , S5 contains all the possible samples.

a) sample space that describes the number of lottery winners out of your group of 5 ={no one won lottery , only one one won lottery , only two won lottery , only three won lottery , only four won lottery, all five won lottery }

no. of samples in sample space = 2**2*2*2*2 = 32

as , each person has two options Yes or No for winning lottery .

b) y is not defined by you . considering it to be the sample space found in part a.

yes , it contains all the outcomes.