Probability

1. Zhi's friend, Sasha, put her chips down on green and waited for the spin. A roulette table has 38 spaces total, with 2 green spaces, 18 red spaces, and 18 black spaces

For any spin of the wheel, what is the probability of the roulette ball NOT landing on green? Answer in fraction.

2. Zhi and her friends needed to decide where to eat. They narrowed their options to eight restaurants, including Zhi's favorite restaurant, Merlin's. To decide where to go, Zhi flipped a coin three times to get eight possible outcomes, where each outcome corresponded to a particular restaurant. The odds in favor of Zhi eating at her favorite restaurant was (A) __________ to (B) __________.

3. Zhi wanted to show her friends the probabilities when spinning the following wheel three times. She used a tree diagram to show the possible outcomes.

How many different outcomes are there when spinning the wheel three times?

4. Zhi and her friends moved on to the card tables at the casino. Zhi wanted to figure out the probability of drawing a face card that was also a diamond.

What is this probability? Enter your answer as a percent, rounded to the nearest whole number.

5. Zhi observes that she could win the game if her next draw from the full standard deck was either an Ace or a black card. She knew her odds of drawing an Ace that was also black were slim, but the chances of drawing either an Ace or a black card was much greater.

What is the probability of drawing an Ace OR a black card? Express your answer as a percent, rounded to the nearest whole number.

6. Zhi had fun playing poker. She needed the next two cards dealt to be diamonds so she could make a flush (five cards the same suit).

If there were fifteen cards left in the deck, and five were diamonds, what is the probability that two cards dealt (without replacement) would both be diamonds? Enter your answer as a percent, rounded to the nearest whole number.

7. Thinking about probabilities, Zhi realized that sometimes one card might fulfill two requirements, such as getting a king of hearts – it would fulfill a requirement of getting a king and getting a heart.

What type of event is this?

8. Zhi plays a game in which she can purchase a ticket and it has several chances, or "catches" to win money. The table below shows the probability of winning at each stage, and how much money the ticket can win at each catch. Every time Zhi plays the game, her ticket is played through each catch, which means we can win money at each stage.

Given the probabilities and payout values in this table, what is the expected value of Zhi's ticket?

9. Zhi went to a blackjack table at the casino. At this table, the dealer is using one standard deck of 52 cards that has just been shuffled. Zhi knows that getting 21, a blackjack, is the best hand possible. She really likes when she is dealt an ace first. Before the second card is dealt Zhi wondered what her chances were of getting another ace if she did not get a face card.

What is the probability that the second card is an Ace, given that it is not a face card? Enter your answer as a percent, rounded to the nearest whole number.