I require assistance with these 11 problems. 1) A Palindrome is a string whose reversal is identical to the string. How
Posted: Wed May 11, 2022 3:33 pm
I require assistance with these 11 problems.
1) A Palindrome is a string whose reversal is identical to the
string. How many six-letter strings from a 26-letter alphabet
are palindromes? (3 Points)
2) Suppose you can pick a final program from one of three
lists. The first contains 9 Python programs, the second
contains 12 Java programs, and the final list contains 8 C++
programs. How many ways are there to choose a program?
(3Points)
3) Suppose a plate lunch at a local restaurant consists of two
scoops of rice, a scoop of mac salad, and two choices of
entrée. The two entrée choices must be different. The
restaurant has three kinds of rice and five different
entrees. How many different variations of the plate lunch are
possible? (6 Points).
(Two plate lunches are different if they differ in at least one
selection. Hint: you can pick different types of rice for
each rice scoop, or they can be the same).
4) Find the number of permutations of the letters in
‘Hawaii’. Just give the formula – you don’t need to calculate
its final value. (6 Points)
5) Imagine that students at UH-Hilo come from all 50 states and
14 US overseas territories, but not from anywhere else. In
this case, what is the minimum number of students, each of whom
comes from one of those states or territories, must be enrolled in
a UH-Hilo class to guarantee that there are at least 3 who come
from the same state or territory? (6 Points)
6) Find the following quantities. Show both the formula
and the value (6 points: 3 points each)
a) P(6,3)
b) C(6,3)
7. An experiment consists of picking at random a bit string of
length 3. Let E1 be the event that the chosen bit string
begins with 1, and let E2 be the event that the bit string chosen
has 2 or more ones. Find P(E1|E2). Show your work (6
points):
8. Three coins are flipped. Let X(t) be the random
variable that equals the number of tails that appear when t is the
outcome. List the possible outcomes of the coin flips, the
values that X(t) will assume for each outcome t, and then list the
probabilities for each possible value of the random variable. (6
points)
9. You have seven cards, numbered 3 through 9, and you pick one
at random. If you pick a card with a prime number, you get 1
point. If you pick a card with a composite (non-prime)
number, you lose 1 point. Find the expected value of the
number of points you get. (6 points)
Hint: it might help to draw a table of possible outcomes and
their probabilities.
10. What is the probability that a random person who tests
positive for a certain blood disease actually has the disease, if
we know that 1 in 400 members of the general population has the
disease, that 98% of those who have the disease test positive for
it, and 1.5% of those who do not have the disease test positive for
it? (6 points)
Note: you do not have to calculate the actual value here.
Just set up the formula and plug in values.
11. A pair of dice is loaded. On the first die, the
probability that a 4 appears is 2/7; the other values appear with a
probability of 1/7. On the second die, the probability that a
3 appears is 3/8, other values appear with a probability of
1/8. What is the probability of 7 appearing as the sum of the
numbers when the two dice are rolled? Is this probability
higher or lower than the probability of rolling a sum of 7 with a
pair of fair dice? (6 points)
Hint: consider each of the ways to roll a 7.
1) A Palindrome is a string whose reversal is identical to the
string. How many six-letter strings from a 26-letter alphabet
are palindromes? (3 Points)
2) Suppose you can pick a final program from one of three
lists. The first contains 9 Python programs, the second
contains 12 Java programs, and the final list contains 8 C++
programs. How many ways are there to choose a program?
(3Points)
3) Suppose a plate lunch at a local restaurant consists of two
scoops of rice, a scoop of mac salad, and two choices of
entrée. The two entrée choices must be different. The
restaurant has three kinds of rice and five different
entrees. How many different variations of the plate lunch are
possible? (6 Points).
(Two plate lunches are different if they differ in at least one
selection. Hint: you can pick different types of rice for
each rice scoop, or they can be the same).
4) Find the number of permutations of the letters in
‘Hawaii’. Just give the formula – you don’t need to calculate
its final value. (6 Points)
5) Imagine that students at UH-Hilo come from all 50 states and
14 US overseas territories, but not from anywhere else. In
this case, what is the minimum number of students, each of whom
comes from one of those states or territories, must be enrolled in
a UH-Hilo class to guarantee that there are at least 3 who come
from the same state or territory? (6 Points)
6) Find the following quantities. Show both the formula
and the value (6 points: 3 points each)
a) P(6,3)
b) C(6,3)
7. An experiment consists of picking at random a bit string of
length 3. Let E1 be the event that the chosen bit string
begins with 1, and let E2 be the event that the bit string chosen
has 2 or more ones. Find P(E1|E2). Show your work (6
points):
8. Three coins are flipped. Let X(t) be the random
variable that equals the number of tails that appear when t is the
outcome. List the possible outcomes of the coin flips, the
values that X(t) will assume for each outcome t, and then list the
probabilities for each possible value of the random variable. (6
points)
9. You have seven cards, numbered 3 through 9, and you pick one
at random. If you pick a card with a prime number, you get 1
point. If you pick a card with a composite (non-prime)
number, you lose 1 point. Find the expected value of the
number of points you get. (6 points)
Hint: it might help to draw a table of possible outcomes and
their probabilities.
10. What is the probability that a random person who tests
positive for a certain blood disease actually has the disease, if
we know that 1 in 400 members of the general population has the
disease, that 98% of those who have the disease test positive for
it, and 1.5% of those who do not have the disease test positive for
it? (6 points)
Note: you do not have to calculate the actual value here.
Just set up the formula and plug in values.
11. A pair of dice is loaded. On the first die, the
probability that a 4 appears is 2/7; the other values appear with a
probability of 1/7. On the second die, the probability that a
3 appears is 3/8, other values appear with a probability of
1/8. What is the probability of 7 appearing as the sum of the
numbers when the two dice are rolled? Is this probability
higher or lower than the probability of rolling a sum of 7 with a
pair of fair dice? (6 points)
Hint: consider each of the ways to roll a 7.