Show:
Theory
Probability rules
Counting techniques
Bayes
Surprise
100
Two events that have no outcomes in common
What is disjoint or mutually exclusive?
100
P(E) = 0.25, P(F) = 0.45, P(E and F) = 0.15 P(E or F) = ???
0.55
100
How many permutations of 3 different digits are there, chosen from the ten digits 0 to 9 inclusive?
720
100
Two cards are chosen at random without replacement from a deck of 52 cards. If the first card chosen is an Ace, what is the probability the second card chosen is also an Ace ?
3/51 or 1/17 or 0.058824
100
In how many different ways can 10 people be seated if the chairs are positioned in a circle?
362880 or 9!
200
The probability that the event F occurs, given that the event E has occured.
What is conditional probability?
200
When 13% of the people are lefthanded, what is the probability that of two randomly selected persons at least one is right-handed?
0.9831
200
There are 10 electable people for a committee. Jones is one of them, and he will be the Chairman. In how many ways can a committee of 5 be chosen from 10 people given that Jones must be Chairman?
126
200
In Exton School, 60% of the boys play baseball and 24% of the boys play baseball and football. What percent of those that play baseball also play football?
40%
200
In a library box, there are 8 novels, 8 biographies, and 8 war history books. If you select two books at random, what is the probability of selecting two different kinds of books in a row?
16/23 or 0.695652
300
An ordered arrangement in which r objects are chosen from n distinct objects and repetition is not allowed.
What is a permutation or nPr?
300
Suppose that E and F are two events and that N(E and F) = 420 and N(E) = 740. P(F | E) = ???
0.568
300
A password consists of two letters of the alphabet followed by three digits chosen from 0 to 9. Repeats are allowed. How many different possible passwords are there?
676000
300
A hat contains three pancakes (really!). One of them looks good on both sides, another one looks burnt on both sides, and the last one is burt on one side only. You randomly place a pancake out of the hat on a plate (eyes closed). You look at the pancake on the plate and the upperside looks good. What is the probability that the other side looks good as well?
2/3 or 0.6667
300
A restaurant offers 5 choices of appetizer, 10 choices of main meal and 4 choices of dessert. A customer can choose to eat just one course, or two different courses, or all three courses. Assuming all choices are available, how many different possible meals does the restaurant offer?
329
400
All outcomes in the sample space S that are no outcomes in the event E.
What is the complement of an event E?
400
You just recieved a shipment of 6 laptops. Two of them are defective. If two laptops are randomly selected, what is the probability that at least one of them does not work?
0.6
400
How many different (nonexisting) words can you compose with the letters from the word 'DROOMOORD'?
3780
400
Consider a well shuffled card deck. What is the probability the second card in the deck is an ace?
4/52 or 1/13 or 0.076923
400
What is the probability that at least two out of six randomly selected persons have their birthday on the same weekday?
0.9572
500
The probability of an event E is approximately equal to the relative frequency of E or, in other words, the number of times event E is observed divided by the number of repetitions of the experiment.
What is the empirical approach?
500
Two dice are rolled and a card is chosen at random from a regular card deck. What is the probability that both dice show an even number and the card is hearts?
0.0625
500
How many different numbers of 4 digits can you make, when 0 is allowed on the first position and the digits must increase in magnitude from left to right?
210 (10C4)
500
Box I contains 7 red and 3 white balls. Box II contains 2 red and 6 white balls. First a box is selected at random (each box is as likely to be selected as the other) and then a ball is drawn from the box. If a red ball is drawn, what is the probability that it came from Box I?
73.7%
500
Jack is cleaning his room and collected 4 math books, 5 chemistry books, and 2 biology books. He places them randomly on a shelf. What is the probability that the books are neatly grouped by subject?
0.000866