For problem #3, since there are "only" 36 possibilities, you can list them all on paper if you want for a pretty straightforward, thoughtless approach. (Can also be relatively fast.) If you're not sure how, consider smaller hypothetical dice with only 3 faces, or something like that.I received a practice worksheet from my professor and I'm wondering if what I did was even close to correct. I could barely figure out even two of them. I feel really dumb right now. I would really appreciate someone informing me on exactly HOW to figure these out, and NOT just the answers so I can walk away actually learning something.

Thank you for any help you can offer.

Here they are:

1.) A bag has 12 marbles of equal size - 5 red, 4 green, 3 blue. Two marbles are removed at random. Compute the following:

a. the event that the first marble is blue and the second is red.

b. the event that the 2 marbles are NOT both blue.

c. if three marbles are selected in order what is the probability that all three marbles selected are blue?

2.) Use combinations in answering each of the following questions and change your answers to the form 1/x where x is rounded to an integer: A seven card hand is dealt from an ordinary deck. What is the probability that...

a. the hand contains two clubs and three diamonds?

b. the hand contains exactly three aces?

3.) A "special" die consisting of one spot on two sides, two spots on two sides, and three spots on two sides is tossed with a "regular" die of six sides. Find the probability that .... (hint: create an addition chart)

a. the sum of the dice is four

b. neither die is a three

c. the same number appears on each die

4.) Place an "E" beside the event if it best represents "E"mpirical probability or an "M" beside the event if it best represents "M"athematical probability.

a. predicting the weather

b. in a 7-card hand, predicting the probability of getting no aces.

c. predicting the chance of being in a car accident.

d. predicting the chance of winning the lottery

e. predicting the probability of tossing a seven with two "loaded" dice

f. predicting the chance of at least 2 people in a group having their birthdays on the same day of the year.

5.) Suppose there are 3000 tickets sold at a raffle. The grand prize is $2,000 and there are 10 other prizes of $100 each and 100 other prizes of $25 each. You buy a single ticket costing $3.50

a. what is the probability that you win the grand prize?

b. what is the probability that you do NOT win any prize?

c. what is the expected value of a single ticket to the individual purchasing the ticket?

6.) John figures that if he stays home for the weekend and studies for his Math exam he will have a 70% change of getting an A. If he does not stay home he figures he still has a 20% chance for an A. John's problem is that he plans to attend a beach party that weekend if it doesn't rain. The weather forecast shows a 40% chance of rain over the weekend. Draw a probability tree diagram for John and answer the following questions. (hint: 1st selection home or beach, 2nd selection A or not A)

a. what is John's chance of getting an A?

b. what is John's chance of not getting an A?

c. if John decides to go to the beach regardless of the weather, what is his chance of an A?

7.) In a game of yahtzee you are left with (1,2,2,2,3) on your second roll. Show the procedure and calculate the "best" probability for tossing each of the following on your third and final roll:

a. full house (three of one kind and two of another kind)

b. small straight (four in a row)

c. yahtzee (all five are the same)

8.) (okay, in this problem there is a pie chart with values: A-14, B-23, C-18, D-35, E-8) The pie chart above is determined by the value shown (not percentages). If the spinner shown is spun at random, what are the following probabilities:

a. spinner lands on A?

b. spinner does NOT land on D?

c. what percent of the time will the spinner land on B or C?

Thanks again for any help

Even though you asked quite nicely and politely for help and explanations, posting 8 questions in one post is really cumbersome. It would be better if you broke it into 8 separate posts. That is the generally accepted practice around here.