HW 1 (Follows Lesson 1)

1. A MHHS student is chosen at random.
Consider the events:
E1= the person chosen is a senior
E2 = the person chosen is a freshman
E3 = the person chosen lives on White Meadow Lake
(a) Are E1 and E2 mutually exclusive? Explain. E1 and E2 are mutually exlcusive because a person cannot be both a freshman and a senior at the same time.
(b) Are E1 and E3 mutually exclusive? Explain. E1 and E3 are not mutually exclusive because a person can be both a senior and and White Meadow Lake resident at the same time.

2. The following table presents the probability distribution of foreign-born residence of the United States and their region of birth:

These are all mutually exclusive events

A. One foreign born indivual is randomly selected...

i. Find P(Latin American) 1 - P(sum of all others) = 1 - (0.488) = 0.512

ii. Find P(Not Asia) = 1 - P(ASIA) = 1 - 0.277 = 0.723

iii. Find P(Europe or Asia) = P(E or A) = P(E) + P(A) = 0.153 +0.277 = 0.43

iv. Find P(Asia or Africa or N.America) P(S) + P(F) + P(N) = 0.277 + 0.03 + 0.027 = 0.3347

B. What type of probabilities are these and why? These a estimated probabilities based on the relative frequency of counts in each category.

3. Musical styles other than rock and pop are becomming more popular. A survey of college students finds that 42% like country music, 30% like gospel music, and 10% like both. Let C = students likes country; Let G = student likes gospel music.

A. Draw a Venn Diagram of this situation These events are not mutually exclusive

B. What percent of college students like either country or gospel? P(C or G) = P(C) + P(G) - P(C and G) = 0.42 + 0.30 - 0.10 = 0.62

C. What percent of college students like country but not gospel? P(C and not G) = P(C) - P(C and G) = 0.42 - 0.10 = 0.32

D. Are Country Music and Gospel Music mutually exclusive events? Show. No, P(C and G) NOT EQUAL zero.

4. Complete on Page 282 #9, 11, 13, and 15