Roll a four sided die twice. Create a table showing the sample space. Find the p

Question

Roll a four sided die twice. Create a table showing the sample space.

Find the probabilities of the following events:

a) The sum is 5

b) The sum is NOT 5

c) The sum is 5

d) The sum is < 5

e) The sum is odd

f) The sum is < 9

g) The sum is >9

h) Exactly one of the two rolls is a 3

i) At least one of the two rolls is a 3

j) What sum(s) have the highest probability of being rolled?

k) What sums have the lowest probability of being rolled?

2. The table shows differences in chosen areas of study for the students in this class by gender.  

Gender

Political Sciences

Fine Arts

Other

Male

9

8

1

Female

8

12

2

5.   Based on the table above, find the probability that a randomly chosen person in this class will be:

a)     male

b)     a student of political sciences

a)     a fine arts student, given that they are male.

c)     a female, given that they are a fine arts student.

b)     not a fine arts student.

d)     a male, or as student of political sciences.

Gender

Political Sciences

Fine Arts

Other

Male

9

8

1

Female

8

12

2

Explanation / Answer

Each of the combinations of (1,1),(1,2),(1,3) etc has probability of 1/16

1. P( sum is 5)=P(1,4)+P(4,1)+P(2,3)+P(3,2)=4/16=1/4

2. P(sum is not 5)=1-P(sum is 5)=3/4

3. P(sum is >=5)=P(sum is 5)+ P(2,4)+P(4,2)+P(3,4)+P(4,3)+P(4,4)=9/16

4. P(sum is <5)=1-9/16=7/16

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