You roll a fair six sided die twice, what is the probability of rolling a 3 and a 5

Given your multiple choices, the probability is 1/32 (but pls see details).

Steps:

A probability is a ratio of the number of successes and the total number of possible outcomes.

The "successes" her are defined to be rolling a 3 and a 5. Here's where the language becomes tiny bit ambiguous: it is unclear if they mean rolling a 3 and a 5 in any order, or rolling a 3 followed by a 5. So what follows are both cases.

Rolling a 3 and a 5 in any order:

number of successful possibilities: 2  (rolling (3,5) or (5,3))

number of all possible outcomes: 6*6 = 36

probability({3,5}) = 2/36 = 1/18  

Rolling a 3 followed by a 5 in that order:

number of successful possibilities: 1  (rolling (3,5) )

number of all possible outcomes: 6*6 = 36

probability({3,5}) = 1/36  << This is the answer to your question

so, converting firstly the mixed fractions to improper fractions and then "adding".

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.