Answer:
I) 
(ii) 
(iii) 
(iv) 
(v)
Step-by-step explanation:
The sample space for an 8-sided fair die rolled twice is:
![[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)]\\](https://tex.z-dn.net/?f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
(a) Possibility diagram of the product of the two numbers appearing on the die in each throw
(b)
I) A prime number
ii) Not a perfect square
Number of Perfect Squares =11
P(Product is Not a perfect square) 
iii) A multiple of 5
Number of Multiples of 5=15
iv) Less than or equal to 21
Product less than or equal to 21=40
v) Divisible by 4 or 6
Products Divisible by 4 or 6= 42
Answer:
43 miles
Step-by-step explanation:
559 divided by 13.
Use the multiplication to check!
Answer:
0.1348 = 13.48% probability that 3 of them entered a profession closely related to their college major.
Step-by-step explanation:
For each graduate, there are only two possible outcomes. Either they entered a profession closely related to their college major, or they did not. The probability of a graduate entering a profession closely related to their college major is independent of other graduates. This, coupled with the fact that they are chosen with replacement, means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which 
is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
53% reported that they entered a profession closely related to their college major.
This means that 
9 of those survey subjects are randomly selected
This means that 
What is the probability that 3 of them entered a profession closely related to their college major?
This is P(X = 3).
0.1348 = 13.48% probability that 3 of them entered a profession closely related to their college major.
Answer: 1/50
Step-by-step explanation:
= 2 * 10^-2 * 2^0
= 2 * 1/10^2 * 1 (2^0=1)
= 2/100
= 1/50
