Combinations and Permutations
Mutually Exclusive and Overlapping Events
Conditional Probability, Independent and Dependent Events
Sequences
Series
100
How many different ways can you rearrange the letters in the word "ALGEBRA".
2520
100
What is the probability that the spinner lands on an even number or a 5? Write your answer as a simplified fraction.
3/5
100
Consider the two-way table below. If event A is viewing Version 2 and event B is Unlike to Buy, are event A and B independent or dependent events? Show how you know.
Dependent, work may vary
100
Find the 52nd term of the sequence:
-2, -5/2, -3, -7/2, ...
a_52 = -55/2
100
Write in sigma notation for the sum of the first 8 terms.
4 + 8 + 16 + ...
sum_(n = 1)^8(4)2^(n - 1)
200
What is the probability that you are dealt a 5-card poker hand that is all face cards? Write your answer as a decimal with four decimal places.
0.0003
200
What is the probability that the spinner below lands on a multiple of 3 or a number greater than 6?
1/2
200
Mrs. G.A. is picking names from her third period class from a hat. There are 22 freshmen and 11 sophomores in that period. She keeps picking names, without replacing them in the hat, until she picks a sophomore. What is the probability that she picks a sophomore on the fourth pick? Write your answer as a decimal rounded to the nearest thousandth.
0.103
200
Find the 8th term of the sequence:
4, -8/3, 16/9, -32/27, ...
a_8 = -512/2187
200
sum_(i = 1)^10((2i)/3 - 2/3)
30
300
There are 18 girls and 15 boys in Mrs. G.A.'s 1st period class. She does a Unit Circle race to see who can fill out a unit circle the fastest, and is awarding first, second, and third place prizes. What is the probability that all three winners are girls? Write your answer as a simplified fraction.
51/341
300
You roll a twelve sided dice. What is the probability that you roll a prime number or a multiple of 6? Write you answer as a simplified fraction.
7/12
300
Consider the two way table below with data about the Titanic. Of the people who did not survive, what is the probability that they were a third class passenger? Of the people who were third class passengers, what is the probability that they did not survive? Write your answers as percentages to the nearest who number, in the correct order.
65%, 74%
300
Find the 24th term of the arithmetic sequence whose 15th term is 104 and 31st term is 200.
a_24 = 158
300
Find the sum of this infinite series, if it exists...
9/5 + 9/20 + 9/80 + 9/320 + ...
12/5
400
Mrs. Frangieh is hanging up the letters of the word PRECALCULUS on her wall. She is randomly picking the letters from a bag as she hangs them from left to right. What is the probability that, when she is done, the two C's are next to each other, the two L's are next to each other, and the two U's are next to each other? Write your answer as a simplified fraction.
4/495
400
You randomly pick a card from a standard deck. What is the probability that you pick a diamond or an odd number card or a card that is a multiple of 3? Write your answer as a simplified fraction.
7/13
400
75% of Algebra 2 Honors students sign up for Precalculus Honors rather than Precalculus. 33% of those PCH students went against their teacher recommendation for math course, while only 4% of the PC students went against their teacher recommendation. What is the probability that a student that went against their teacher recommendation is in PCH? Write your answer as a decimal rounded to the nearest hundredth.
0.96
400
Write an explicit rule for the geometric sequence with the following terms:
a_5 = -5/3
a_2 = -45
a_n = -135(1/3)^(n-1)
400
The sum of the first n terms of the series below is -9831. How many terms are in the series?
-3 + 12 - 48 + 192 ...
n = 7
500
You are rolling four 6-sided dice. What is the probability that you roll at least 2 fours?
19/144
500
364 people were surveyed to see if they drank coffee or tea. It is possible that the people surveyed drink only coffee, only tea, both or neither. 187 people said they drink tea, 221 said they drink coffee, and 52 said they drink neither. What is the probability that a someone from the survey drinks coffee or tea? Write your answer as a simplified fraction
6/7
500
Mrs. G.A. teaches Algebra 2 Honors and Calculus. 68% of her students are in Algebra 2H. 91% of her Calculus students are passing the class, and 97% of her Algebra 2 Honors students are passing the class. A student comes in during tutorial, upset that they are failing. What is the probability that this is a 2H student? Write your answer as a percentage rounded to the nearest whole number.
41%
500
Write an explicit rule for the arithmetic sequence with the following terms:
a_40 = -591/10
a_19 = -138/5
a_n = -3/2n + 9/10
500
Evaluate the sum:
sum_(k = 4)^18 -11/12 + 5/3k
1045/4