MAT 130 BCC Event Probability Permutations & Distinguishable Arrangements Exam Practice

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Mat 130 Test 3 Spring 2021
Name:_______________________
This is a Take-Home test; please read the instructions in the provided document.
To get full credit you have to show work for all problems except problems 1-6.
Decide whether each statement is true or false. (2 points each)
1. The probability of the complement of an event can be a number strictly smaller than zero.
2. In the context of counting problems, arrangements are called permutations.
3. If the odds in favor of 𝐸 are 𝑎 to 𝑏, then P(E) =
a
.
a−b
Evaluate each expression. (4 points each)
4.
5.
6.
!”#!
!!”!
10!
6 ⋅ (10 − 3)!
!”!
!∙ !”!! !
Solve the following problems.
7. Suppose we want to form four-digit numbers using the set of digits {0,1, 6, 7, 9}. For example, 9071
and 7710 are such numbers but 0716 is not.
How many such numbers are possible? (7 points)
8. How many 5-letter “words” without repeated letters are possible using the English alphabet?
Assume that any 5 letters make a word and note that the English alphabet has 26 letters. (7 points)
9. Find the number of distinguishable arrangements of the letters of the word ANNABELLA. (7 points)
10. Determine the number of possible settings for a row of five on-off switches under each condition.
(9 points)
(a) There are no restrictions.
(b) The first and fifth switches must be set the same.
(c) No two adjacent switches can both be off.
11. If you toss 8 fair coins, in how many ways can you obtain at least one head? (7 points)
12. How many of the possible 5-card hands from a standard 52-card deck would contain only cards of a
single suit? (7 points)
13. Suppose two fair dice are rolled. Find the probability of rolling the following sums. (9 points)
(a) 7
(b) 3
14. A fair coin is flipped 4 times. Find the expected number of tails. (7 points)
15. For the experiment of drawing a single card from a standard 52-card deck, find the odds against the
event “heart or face card”. (7 points)
16. Six people (three married couples) arrange themselves randomly in six consecutive seats in a row.
Find the probability of each of the following events. (9 points)
(a) Each man will sit immediately to the left of a woman.
(b) The women will be in three adjacent seats. (NOTE: the men do not have to be adjacent)
17. Convert 2346 to base 16. (6 points)
BONUS (5 points)
Let two cards be dealt successively, without replacement, from a standard 52-card deck. Find the
probability of the event “the first card is the ace of hearts and the second is black”.
MAT-130-001 Test 3 Take-Home Instructions Spring 2021
1. This test is “open book” which means you are permitted to use any materials handed
out in class, your own notes from the course, the text book, and anything on Moodle.
2. The test must be taken completely alone. Showing or discussing it with anyone is
forbidden.
3. You may not consult any external resources. This means no internet searches, materials
from other classes or books or any notes you may have taken in other classes etc. You
may not use Google or any other search engines for any reason.
4. You may not consult with any other person regarding the test. You may not check your
test answers with any person. You may not discuss any of the materials or concepts in
MAT-130 with any other person.
5. The test is due Wednesday, May 12, 2021, ABSOLUTELY no later than 4:45 P.M.
The penalty for a late submission will be up to 50% off the earned grade, depending on
how late the submission is. For example an earned grade of 100 will be 50.
A grade of zero will be given if any of the prohibited sources have been used.
6. ONLY online text, pdf, jpg, and jpeg formats will be accepted.
7. Please clearly label the answers and make sure that you have uploaded (or sent, if
you can’t upload to Moodle) everything, including work.

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Permutations

event probability

expected number

distinguishable arrangements

possible settings

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