Assume that you toss a fair six-faced die two times. 1.What is the probability t
ID: 3152950 • Letter: A
Question
Assume that you toss a fair six-faced die two times.
1.What is the probability that you get an even number at the first toss? (Show work and write the answer in simplest fraction form)
2. What is the probability that the sum of the two tosses is at least 7, given that you get an even number in the first toss? (Show work and write the answer in simplest fraction form)
3. If event A is “Getting an even number in the first toss” and event B is “The sum of two tosses is at least 7”. Are event A and event B independent? Use mathematical expression to justify your answer.
Explanation / Answer
Assume that you toss a fair six-faced die two times.
1.What is the probability that you get an even number at the first toss? (Show work and write the answer in simplest fraction form)
Total outcomes =36
Sample space to get an even number at the first toss
1
2
3
4
5
6
2
(2, 1)
(2, 2)
(2, 3)
(2, 4)
(2, 5)
(2, 6)
4
(4, 1)
(4, 2)
(4, 3)
(4, 4)
(4, 5)
(4, 6)
6
(6, 1)
(6, 2)
(6, 3)
(6, 4)
(6, 5)
(6, 6)
probability that you get an even number at the first toss = 18/36 =1/2
2. What is the probability that the sum of the two tosses is at least 7, given that you get an even number in the first toss? (Show work and write the answer in simplest fraction form)
Sample space to get at least 7, given that you get an even number in the first toss
1
2
3
4
5
6
2
(2, 5)
(2, 6)
4
(4, 3)
(4, 4)
(4, 5)
(4, 6)
6
(6, 1)
(6, 2)
(6, 3)
(6, 4)
(6, 5)
(6, 6)
P=12/36 =1/3
3. If event A is “Getting an even number in the first toss” and event B is “The sum of two tosses is at least 7”. Are event A and event B independent? Use mathematical expression to justify your answer.
Outcomes for Two Dice
1
2
3
4
5
6
1
(1, 1)
(1, 2)
(1, 3)
(1, 4)
(1, 5)
(1, 6)
2
(2, 1)
(2, 2)
(2, 3)
(2, 4)
(2, 5)
(2, 6)
3
(3, 1)
(3, 2)
(3, 3)
(3, 4)
(3, 5)
(3, 6)
4
(4, 1)
(4, 2)
(4, 3)
(4, 4)
(4, 5)
(4, 6)
5
(5, 1)
(5, 2)
(5, 3)
(5, 4)
(5, 5)
(5, 6)
6
(6, 1)
(6, 2)
(6, 3)
(6, 4)
(6, 5)
(6, 6)
P( A) =1/2
P( B) =21/36
P( B/A) =1/3 ( from previous answer)
P( B/A) P( B)
The event A and event B are not independent.
1
2
3
4
5
6
2
(2, 1)
(2, 2)
(2, 3)
(2, 4)
(2, 5)
(2, 6)
4
(4, 1)
(4, 2)
(4, 3)
(4, 4)
(4, 5)
(4, 6)
6
(6, 1)
(6, 2)
(6, 3)
(6, 4)
(6, 5)
(6, 6)