Question

Show your work!

2.   We did a poll of students in a BUS 232 class. The students were asked to name their favorite color. The result is shown in Table 2.

Table 2

     Favorite Color

	Red	Blue	Purple	Total
Female	2	2	0	4
Male	0	3	1	4
Total	2	5	1	8

Number of E whoare∈favorof F

Hint: Conditional Probability Rule: P (F | E) =

Totalnumberof E

Suppose that one student is selected at random from the group. (4 points) What is the probability as a fraction in the simplest form that:

1. it will be a male? P (male) =
2. it will be a female who likes red? Hint: This is NOT a conditional probability.
   16. (a female who likes red) =
3. it will be someone who likes blue given that we know that it is a male?
   16. (someone who likes blue | male) =
4. it will be someone who likes red given that we know that it is a female?

.

16. (someone who likes red | female) =

3.   Suppose you roll a fair die three times. What would be the probability of getting ONE three times? Hint: Use the law of large number, which is the theoretical probability. Show the answers as a fraction in the simplest form. (2 point)

P (1 for the first roll, 1 for the second roll and 1 for the third roll roll) =

Answer 1

2.

a. probability it will be a male = Number of male students / Total number of students = 4/8 = 1/2

P(Male) = 1/2

b.probability it will be a female who likes red = Number of female students who likes red / Total number of students = 2/8 = 1/4

P(Female who likes red) = 1/4

c.probability it will be someone who likes blue given that we know that it is a male

= Number male students who likes blue / Number of male students = 3/4

P(someone who likes blue | male) = 3/4

d. .probability it will be someone who likes red given that we know that it is a female

= Number female students who likes red / Number of female students = 2/4 = 1/2

P(someone who likes red | female) = 1/2

3. Suppose you roll a fair die three times. The probability of getting ONE three times.

P(1 for the first roll) = Probability of getting one when a die is rolled first time = Number of events favoring getting one / Total number of events = 1/6

Result of rolling a die on a given time does not dependent on the result of the previous roll

P(1 for the second roll) = Probability of getting one when a die is rolled second time =1/6

P(1 for the third roll) = Probability of getting one when a die is rolled third time = 1/6

P (1 for the first roll, 1 for the second roll and 1 for the third roll roll)

= P(1 for the first roll) x P(1 for the second roll) x P(1 for the third roll)

(1/6) x (1/6) x (1/6) = 1/216

Probability of getting ONE three times = 1/216