An urn contains 90 balls. It is known that 30 are red and that each of the other 60 is either yellow or black. One ball will be drawn at random from the urn. Consider the following four options: Option 1 We receive $1,000 if a red ball is drawn. Option 2 We receive $1,000 if a yellow ball is drawn. Option 3 We receive $1,000 if a yellow or black ball is drawn. Option 4 We receive $1,000 if a red or black ball is drawn. a Explain why most people prefer option 1 over option 2 and also prefer option 3 over option 4. b If we prefer option 1 to option 2, explain why we should also prefer option 4 over option 3.

A bucket has 4 blue ping pong balls, 3 pink ping pong balls and 7 yellow ping pong balls. One ping pong ball is chosen at random from the bucket. Determine the probabyof each of the following.  a. P (blue ping pong ball) b. P (yellow ping pong ball) c. P ( not a pink ping pong ball)

You are going to a bakery and they are selling bread (B), doughnuts (D) and cookies (C). A. If you are only going to buy two different items, list all of the permutations. B. If you are only going to buy two different items, list all of the combinations.

At a carnival, an individual can win a prize by choosing a rubber duck from a pond with "Win" written on the underside of the duck. There are a total of eight ducks with "Win" written on the underside of the duck, and there are 17 ducks with "Lose" written on the underside of the duck. After each pick, if a prize is won, the duck is replaced in the pond. If a prize is not won, then the duck is again placed back into the pond. If an individual makes four picks, what is the probability the individual will win a prize exactly one time? (4) (0.32) (0.68) 1! 4! (0.32)¹ (0.68)³ O2(0.32)(0.68) (0.32) (0.68)³

A teacher will randomly award three students with extra credit. How many possible ways can the teacher pick these three students from a class of 20 students?

.When purchasing a ticket for the PowerBall lottery game a player chooses 5 distinct numbers between 1 and 69 (inclusive). The order in which the numbers are chosen does not matter. In addition, the player chooses one number between 1 and 26 (inclusive) to match the "powerball." How many different powerball tickets are possible?

A standard deck of cards has 52 cards in four suits: spades, hearts, diamonds, and clubs. Spades and clubs are black; hearts and diamonds are red. Each suit has 13 cards: 2 through 10, Jack, Queen, King, Ace. The "face cards" are the Jack, Queen, and King. Robby Billity shuffles a standard deck and draws one card. Then Robby Replaces the card, shuffles again, and draws another card. He repeats this procedure for a total of 1000 draws. About how many times would we expect Robby to draw these cards?  A) the ace of spades B) a face card in any suit

Imagine you draw a marble from a bag with one green, one red, one blue, and one purple marble 9 times.  You replace the marble you drew every time.  You record the color each time you draw.  How many outcomes are possible?