Counting
A restaurant has 2 appetizers, 4 main courses, and 3 desserts to choose from. How many different 3 course meal possibilities are there?
24
You roll a dice. What is the probability of rolling a 4?
1/6
You have 5 red, 3 green, and 2 blue marbles. What is the probability of choosing a green or a red?
8/10 or 4/5
A study shows that 35% of fish caught in a lake have high levels of mercury. Suppose that 10 fish were caught, what is the probability that 8 of them have high levels of mercury?
.0043
You are playing a game where you flip one coin. If it lands on heads you get 5 points. If it lands on tails you lose 3 points. What is the expected value for this game?
1
In how many ways can a committee of five members be chosen from a group of 20?
15,504
Are the following events independent or dependent? Choosing a color of a mountain bike and choosing a trail to ride on.
Independent
There are four nickels, five dimes, and three quarters in your pocket. You randomly pick a coin. It is a nickel or a dime.
9/12 or 3/4
A recent survey showed that 65% of college students drink coffee in the mornings. If a sample of 20 students are chosen, what is the probability that 14 students will drink coffee?
.1712
A company plans to invest in a particular construction project. There is a 35% chance that it will lose $40,000, a 40% chance that it will break even, and a 25% chance that it will make a profit of $65,000. How much can the company expect to make or lose on this project?
$2,250
How many ways can a president, vice president, secretary, and treasurer be chosen from a class of 30 people?
657,720
Find the probability of selecting a blue marble, replacing it, then a yellow marble from a box of 8 blue marbles and 5 yellow marbles.
40/169
You roll a dice. What is the probability the result if greater than 4 or even?
4/6 or 2/3
A study shows that 72% of high school seniors have a job. If 22 seniors are surveyed, what is the probability at least 21 of them have a job?
.0069
Find the expected value for a game where you are rolling a single die. If you roll an even number, you get 4 points. If you roll a 5, you lose 3 points, if you roll a 1 or a 3, you get 0 points.
1.5
In how many ways can six people be seated in a row of six seats?
720
Find the probability of selecting a blue marble, not replacing it, then a yellow marble from a box of 8 blue marbles and 5 yellow marbles.
10/39
A bag contains five yellow tennis balls numbered one to five. The bag also contains three green tennis balls numbered one to three. You randomly pick a tennis ball. It is yellow or has an odd number.
7/8
The probability of a student passing a Math 4 Exam is 85%. Given there are 28 students in a class, what is the probability at least 27 of them pass?
.0627
A carnival game costs $3. The game contains 7 ducks numbered 1-7. If you pick and even duck, you win $4. If you pick a duck numbered 1 or 3 you win nothing. If you pick a duck numbered 5 or 7 you win $2. What is the expected value of the game?
$-0.72
In a talent show, five semi-finalists are chosen from 46 entries. In how many ways can the semi-finalists be chosen?
1,370,754
A bag contains 4 blue, 6 red, and 2 yellow marbles. What is the probability of drawing one blue, one red, and one yellow if you do not replace the marble after each draw.
2/55
A basket contains four apples and six peaches. One of the apples and four of the peaches are rotten. You randomly pick a piece of fruit. It is rotten or it is a peach.
7/10
The probability a family watches fireworks at the 4th of July show is 54%. if 7 families are surveyed, what is the probability that at most 2 of them watch the show?
.1663
“Wheel of Fortune” just got a new wheel! On it there are 6 slots worth $200, 15 slots worth $400, 2 slots worth $600, 6 slots with no money, 1 slot with $1000 and 1 slot with a car worth $20,000. a. What is the expected winnings on one turn (cash and prizes)?
$948.40