Basic stats/probability problems help please -___-

I have a couple questions regarding, well, a couple questions.

1.) A jar contains four coins: a nickel, a dime, a quarter, and a half-dollar. Three coins are randomly selected from the jar.
(a) List the simple events in S. (Use N for nickel, D for dime, Q for quarter, and H for half-dollar.)
(b) What is the probability that the selection will contain the half-dollar? (Enter an exact number as an integer, fraction, or decimal.)
(c) What is the probability that the total amount drawn will equal 55¢ or more? (Enter an exact number as an integer, fraction, or decimal.)
okay, forgive me if this is a dumb question, but with a question like this, does order matter? For instance, would NDQ be different than QDN?

also,

2.) A student prepares for an exam by studying a list of 10 problems. She can solve 3 of them. For the exam, the instructor selects 2 questions at random from the list of 10. What is the probability that the student can solve all 2 problems on the exam? (Enter an exact number as an integer, fraction, or decimal.)

My answer is 0.0333. With my teacher, I only get three chances to get the answer correct, so I just wanted to see if this was correct.


Thank you in advance :)

Hey spark062.

For number 2, it's best if you draw a tree diagram.

You will have four leaves corresponding to no matches, 1 match, and 2 matches.

For the branch with two matches we have the first question with a probability of 3/10 since we start off with 10 questions of which 3 of them are ones we know. The second one however has only 9 choices (since we picked 1) with 2 of them being ones we can solve.

Both choices are independent which means we can apply P(A and B) = P(A)P(B) with P(A) = 3/10 and P(B) = 2/9. P(A and B) = 3/10*2/9 = 6/90 or given by R,

> 6/90
[1] 0.06666667

How did you come to the answer that you got? (Also can you show us your working for Q1 to get specific answers on those)?