Exam 1

W. Li

problem 4:

.4

Assume you have a small bag of M&Ms in three varieties: 40 of milk chocolate, 35 of peanut, and 25

.35

. 25

of pretzel. Suppose you don't like the pretzel flavor, so every time you pick a pretzel M&M, you put it

back into the bag. If you pick any of other kinds, milk chocolate or peanut M&M, you eat it right away.

Assume you pick only one M&M at a time, and you will select three times (without looking). Find the

probability (in decimals) that: (15 points total)

16198

a) You will eat exactly one M&M. (5 points)

Second dau

First

as/ICC

as /98

(25 ) (85 ( 8) . 048

24/5

25/g9

draw

?S/ ico

b) You will eat at least 2 M&Ms. (5 points)

IS(

Second

10C

45 : . $768

clicw

Third drav

c) You won't eat any of the M&M. (5 points)

= . 016

Problem 5:

Susan has been keeping statistics on lost pets in her neighborhood. She has determined that 80% of

the "lost" pets turn up within a couple of weeks. She is tired of helping her friends look for pets for

free, so she decides to offer her neighbors a lost pet insurance plan. If they pay her $5 to join her plan,

she will look for the pet that go missing. If she cannot find the pet within a certain period (e.g., a

week), she will pay the owner $50. Can she make money based on her plan? (10 points total)

a) Give the probability distribution for Susan's plan in tabular form. (2 points)

X

5

-50

P(x )

8

. 2

b) Find the expected value and the standard deviation for Susan's plan. (5 points)

u: 5 (. 8)

1 (- So ) (. 2) =-16

829 6 t9 + 3. = [(? ) (9 - 0 -1 * [ (8 )2 ( 9-9 ) = 20

V 6as : 25 . 06

c) How much should Susan charge if she would like to make $10 per client on average? (3 points)

X

6

p(x )

S

. ?

$10 : .89 - 50(.8)

V1

she should charge $es

if she would like to

make sto per client