Assignment12 1

APStatistics
Statistics Assignment 12: Rules of Probability
Directions: Complete the assignment on your own paper. Clearly label each answer. (34 points)

1. You roll a pair of standard dice. Create the sample space for a single roll of the dice and use the sample space to compute the following probabilities. (8 points)

a. Create a sample space.
{1, 2, 3, 4, 5, 6}
b. P (getting a 1 on the first die or getting a 6 on the second die)

1/6+1/6= .333

c. P (getting a 3 on the second die given that you got a 2 on the first die)

1/6= .167

d. P (getting an odd number on the first die and a value greater than 4 on the second die)

(1/2)(1/3)= .167

2. Below is some hypothetical data on the voting preferences of individuals of different religious affiliations by political party in 4 southern states in the Fall Election of 2002.

Vote in 2002 Election
Roman Catholic
Southern Baptist
Methodist
Totals
Democrat
5600
7000
6000
18600
Republican
4900
8700
4600
18200
Independent
2000
1600
1700
5300
Totals
12500
17300
12300
42100

Use this information to compute the following probabilities: (8 points)

a. P (Vote for Independent Party)

(5300/42100)= .126

b. P (Vote for Democrat Party or Methodist)

(18600+12300-6000)/42100= .591

c. P (Vote for Republican Party, given that individual is Methodist)

4600/12300= .374
d. P (Southern Baptist, given that individual was of the Independent Party)

1600/5300= .302

3. In a random sample of male and female graduates of the New York School for the Arts between the ages of 22-35 you know that: the probability a man is a ballet dancer is 0.245. the probability a woman is a musical performer is 0.365 the probability a man is a musical performer, given that he’s a ballet dancer is 0.250. the probability a woman is an actress is 0.550. the probability a woman is an actress, given that she’s a musical performer is .785.
Compute the following probabilities: (6 points)
a. P (man is a ballet dancer and a musical performer)

.245(.250) = .0613