A license plate consists of three letters followed by four numbers. How many license plates are available if the number 7 is not allowed to be used. (Numbers can repeat; letters cannot)
What is 102,351,600 different plates are available
100
What is the probability of a family having five boys born consecutively?
What is 1/32
100
Take a look at the chart on the board. If one person is selected at random find the probability the person selected: Does not prefer Coke
What is 150/260 or 15/26
100
One card is drawn from a deck. Find the probability that the card is: a face card or a 9
What is 4/13
100
Three thousand raffle tickets are sold for $3 each. Three prizes will be awarded: one for $2500 and two for $1500 each. Kelly purchases one ticket. Determine her expected value.
What is -$1.17 (Kelly is expected to lose $1.17 for each ticket she purchases)
200
Evaluate (using a calculator at the very end):
197!/194!
What is 197 * 196 * 195 = 7,529,340
200
One card is randomly selected from a deck of 52 cards. Find the odds in favor and the odds against getting a queen.
What is 1:12 in favor; 12:1 against
200
Take a look at the chart on the board. If one person is selected at random find the probability the person selected: Prefers Pepsi, given that a man was selected
What is 45/136
200
One card is drawn from a deck. Find the probability that the card is: red, given that the card is a heart
What is 1
200
During July in Seattle, the grass grows 1/2 inch on every sunny day and 1/4 inch on every cloudy day. 75% of the days are sunny and 25% are cloudy. Find the expected amount of grass growth on a July day in Seattle.
What is 0.4375 inches
300
How many distinct permutations can be formed using the letters in Tennessee?
What is 3780 distinct permutations
300
A die is rolled. What is the mathematical probability of rolling a number less than 7?
What is 1
300
The probability of a flood in any given year in a region prone to flooding is 1/5. What is the probability of a flood for three consecutive years.
What is 1/125 or 0.008
300
One card is drawn from a deck. Find the probability that the card is: a queen, given that the card is a face card.
What is 4/12 or 1/3
300
Cal and Phil play the following game: Cal picks a card from a deck of cards. If he selects a club, Phil gives him $10. If not, he gives Phil $4. Find Cal's expected gain or loss.
What is -0.5
400
You have 45 DVD's and you are planning to take 7 of them on a weekend vacation. How many different collections of 7 can you take?
What is 45,379,620 different collections
400
State one difference between mathematical probability and empirical probability.
What is in empirical probability an experiment is conducted (answers may vary and are up to my discretion)
400
The probability of a flood in any given year in a region prone to flooding is 1/5. What is the probability of no flooding for four consecutive years?
What is 256/625 or 0.4096
400
One card is drawn from a deck. Find the probability that the card is: between a 7 and a jack
What is 12/52 or 3/13
400
In a certain game, you roll a single die. If you roll a 6 you get $3, if you roll a 5 you get $2, and if you roll a 4 you get $1. Otherwise you get nothing. If it costs $1.50 to play, what is your expected gain or loss?
What is 0.25
500
How many different committees can be formed from 22 Democrats and 19 Republicans if each committee is made up of 5 Democrats and 5 Republicans?
What is 22C5 * 19C5 = 306,211,752
500
A bag contains 130 jellybeans. One is picked from the bag, the color recorded, and then placed back in the bag. This is done 110 times and 27 times a red jellybean was drawn. Find the empirical probability of drawing a red.
What is 27/110
500
The probability of a flood in any given year in a region prone to flooding is 1/5. What is the probability of a flood occurring at least once in the next four years?
What is 1-(256/625) or 1-0.4096 = 0.5904 (a 59% of a flood occurring at least once)
500
One card is drawn from a deck. Find the probability that the card is: a king or a spade
What is 4/13
500
A political discussion group consists of 11 Democrats and 9 Republicans. Four of them are selected to attend a conference. Find the probability that the selected group will consist of all Republicans.
What is 42/1615 (show setup of the problem and the answer)