Freshman
In how many ways can the five letters of the word LATIN be arranged in a row?
What is... 120
A, B, and C are randomly selected real numbers between 0 and 6. What is the probability that A is between 1 and 3, B is between 2 and 4, and C is between 3 and 5? Give your answer as a reduced fraction.
What is ... 1/27
A deck of cards consists of 52 cards, Ace, 2, 3, ... 10, Jack, Queen, and King, in each of four suits, Clubs, Diamonds, Hearts, and Spades. What is the probability that if you draw one card that it is either a Spade or an Ace?
What is... 4/13
An unfair coin comes up heads 60% of the time. If the coin is tossed 5 times, what is the probability of getting exactly 3 heads and 2 tails? Give an exact answer.
What is... 216/625
Sammy hits a homerun on the average of once every 8.4 times at a bat. Barry hits a homerun on the average of once every 9.6 times at bat. If both player come up to bat once in the same inning, what are the odds that at least one of them will hit a homerun that inning? Give your answer as a reduced fraction.
What is... 425/1591
How many positive 8 digit numbers can be formed using each of the digits from {1, 2, 3, 4, 5, 5, 6, 6}?
A piece of string, 25 inches long, is cut at a random point. What is the probability that one piece of string is at least 5 inches longer than the other piece of string? Give your answer as a reduced fraction.
What is... 4/5
Three hundred of the 500 juniors at Tom Cruise High School are girls, and 250 of the 400 seniors are girls. A name is drawn at random from the combined junior/senior class list. If the name is that of a girl, what is the probability that she is a senior?
The Springstead Volunteer Fire Department is having a raffle for a fishing boat valued at $8,500. Five thousand raffle tickets have been printed and all of them were sold at $10.00 a ticket. If Mr. Angler buys a single ticket, what is the expected value of his ticket purchase?
What is... -8.30
Draw one card from a standard 52-card deck. If it is a heart, stop. If not, put the card backin the deck, shuffle the deck, and draw again, replacing and shuffling if you fail to get a heart. Keep drawing until you get a heart. What is theprobability that it will take you at least four draws to get the first heart?
What is... 27/64
A nickel is tossed in the air three times. It lands flat on the floor. What is the probability that all three outcomes are the same, that is, three heads or three tails?
What is... 1/4
A circle with a radius of two is randomly placed so that its exact center is inside a 10 by 10 square. What is the probability that the entire circle is within the square?
If two different positive integers less than or equal to 50 are chosen at random, what is the probability that the difference between them is less than 10?
What is... 81/245
The probability that somebody has a certain trait is 0.10. When people are tested for the trait, the test is not always accurate. If somebody has the trait, the probability that the test is correct is 0.98. If somebody does not have the trait, the probability that the test is correct is 0.94. If somebody tests positive for the trait, what is the probability that they actually have the trait? Give your answer as a simplified fraction.
What is... 49/76
An automobile has a full 16 gallon tank of gas and gets 23 miles per gallon of gasoline. One day Tom drives the car some random distance but not mroe than 150 miles. The next day Sue drives the same car some random distance but not more than 200 miles. What is the probability that after these two days of driing there is less than one-half a tank of gasoline left? Give an exact answer as a reduced fraction.
What is... 91/200
Given a 15-gon (a polygon with 15 sides), how many triangles can be formed using diagonals and at least one side of the polygon?
Sheila arrives at school at a random moment between 9:00 and 9:30. Shelly arrives at a random moment between 9:10 and 10:00. What is the probability that Sheila arrives before Shelly?
What is... 13/15
There are 13 clubs in a standard deck. Drew is drawing one card at a time from the deck, replacing and shuffling after each draw. Flossie is awarded 3 points if the drawn card is a club, whereas Ned is awarded 1 point if it is not a club. The first player to reach 21 points is declared the winner. The score is currently Flossie: 15, Ned: 19. Find Flossie's probability of going on to win from this point.
What is... 5/32
Harry and Nancy are gambling. They toss a fair coin six times. If the number of heads is one less than a multiple of three, then Harry wins from Nancy one dollar per head. If the number of heads is two less than a multiple of three, then Nancy wins from Harry one dollar per head. Who is expected to win the game, and what is the expected value of the amount s/he will win if the game is played once? Give your answer in dollars, rounded to the nearest cent.
What is... Nancy, $0.09
Five coins are in a bag, each of which has a 50% chance of being counterfeit. Given that at least two of the coins in the bag are counterfeit, what are the chances of drawing two coins at random and each is counterfeit?
What is... 4/13
You are given 5 different consonants and 3 different vowels. From all possible six letter words using a letter from the list at most once, what is the probability that a word chosen at random will have a consonant as the first letter, and will contain at least two vowels?
What is... 15/28
C and D are randomly selected real numbers between -3 and 3. X is the integer closest to C and Y is the integer closest to D. What is the probability that X + |Y| > 0?
What is... 2/3
Cards are drawn, one at a time with replacement, from a standard 52-card deck. What is the probability that the second spade is obtained on the sixth draw?
What is... 405/4096?
A square target, 200 feet on a side, is marked on the ground for a skydiver to try to hit. On three of the vertices of the square, red flags are placed. Bull's-eye McDuffy is going to skydive from an altitude of 8,000 feet above the target. Bull's-eye will win a $50,000 prize if he lands at any point of the square target that is at least 100sqrt2 feet away from each of the 3 corners containing a flag. If Bull's-eye is equally likely to land at any point of the target, what is the probability that he wins the $50,000 prize? Give your answer rounded to the nearest thousandth.
What is... 0.107
A certain trait is simple dominant, which means that everybody receives one gene from each parent relevant to the trait, and they have the trait if either one or both of those genes is for the dominant trait. They only do not get the trait if they get two recessive genes, one from each parent. For a particular simple dominant trait, exactly half of the population has the dominant trait and half has the recessive trait. If two people with the dominant trait have a child, what is the probability that the child will have the dominant trait? Give an exact answer?
What is... 2sqrt2 - 2