WGU C960 OBJECTIVE ASSESSMENT V1 & V2
NEWEST 2026 TEST BANK| C960 DISCRETE
MATHEMATICS II OA EXAM REVIEW WITH
COMPLETE REAL EXAM QUESTIONS AND CORRECT
VERIFIED ANSWERS/ GRADED A+ (MOST RECENT!!)
C960 DISCRETE MATH II OA V1.
There are two coins, one fair and one biased. The biased coin comes up
heads with a probability 0.8 and tails with a probability 0.2. One of the
coins is selected at random and flipped ten times. The results of the coin
flips are mutually independent. The result of the 10 flips is H, T, T, H, H,
T, H, H, T, H.
What is the probability that the coin flipped was the biased coin? (Round
to the nearest tenth.) - ANSWER - 0.3 OR 30%
P(HHTTTHTHHT | B)=0.86 ×0.24
P(HHTTTHTHHT | F)=0.510
P(B)=P(F)=0.5
(0.8⁶ × 0.2⁴) × 0.5 / (0.8⁶ × 0.2⁴) × 0.5 + (0.5¹⁰) × 0.5
A life insurance company issues standard or preferred policies. Of the
company's policyholders, 60% have standard policies and a probability
of 0.01 of dying in the next year, and 40% have preferred policies and a
probability of 0.08 of dying in the next year. A policyholder dies in the
next year.
pg. 1
,What is the conditional probability of the deceased having a preferred
policy? - ANSWER - P(S) = 0.60, P(P) = 0.40,P(D|P) = 0.08, P(D|S) =
0.01, and the answer is 0.8421.
P(S)=0.60 (probability of having a standard policy)
P(P)=0.40 (probability of having a preferred policy)
P(D|P)=0.01 (probability of dying given a standard policy)
P(D|S)=0.08 (probability of dying given a preferred policy)
(0.08 × 0.40) / (0.08 × 0.40) + (0.60 ×0.01) = 0.8421
Which formula is the expected value of the random variable Y? -
ANSWER - (upper limit)∑(index = lower limit),
∑(s∈Y), | Y (s) | p(s)
There are four different colored balls in a bag. There is equal probability
of selecting the red, black, green, or blue ball. What is the expected
value of getting a green ball out of 20 experiments with replacement? -
ANSWER - 5
20 × .25
A company has three active projects: Domino, Falcon, and Giant. There
are 19 employees charging time to Domino, 16 to Falcon, and 15 to
Giant. Those totals include 8 employees charging both Domino and
Falcon, 6 charging both Falcon and Giant, and 7 charging both Giant and
pg. 2
,Domino. Included in those subtotals is the 4-person IT team, all of
whose members charge all three projects.
How many employees are working on the projects? - ANSWER - 33
Total employee = 19 + 16 + 15 = 20
Charging employees = 8 + 7 + 6 = 21
Duplicate charges = 21 - 4 = 17
Actually working employees = 50 - 17 = 33
A random experiment consists of tossing a fair six-sided die repeatedly.
How many tosses are required to be certain that the probability that at
least one '6' appears is greater than or equal to 1/2? - ANSWER - 4
The probability of not getting a 6 in one toss is P(not 6)=56
Now, applying this value into the expression we found in step(1),
⇒1−(P(not 6))n≥1/2
⇒1−(5/6)n≥1/2
⇒−(5/6)n≥−1/2
⇒(5/6)n≤1/2
⇒ln(5/6)n≤ ln(12)
⇒n×ln(5/6)≤ ln(1/2)
⇒n≤ ln(1/2)ln(5/6) = 3.80 round to 4
pg. 3
, An encryption scheme uses the numerical position of a letter in the
alphabet to encrypt characters, e.g., A=1, D=4, Z=26, etc., and spaces
are ignored. What is the encoding of "HAPPY BIRTHDAY" using this
technique? - ANSWER - 8116162529182084125
An individual has chosen the public key of N = 187 = 11 x 17 and e = 3.
What is the private key using RSA encryption? - ANSWER - 107
To find the RSA private key d, you calculate the modular inverse of the
public exponent e with respect to (p−1)(q−1), where p and q are the
prime factors of N. Here, N=187 is factored into p=11 and q=17. Thus,
ϕ(N)=(11−1)(17−1)=160. The private key d satisfies 3d≡1mod160.
Using the Extended Euclidean Algorithm, we find d=107, which is the
modular inverse of 3 modulo 160.
Assume that a test for a disease gives a positive result for 1.5% of people
who do not have the disease, but does not test negative if the person has
the disease.
What is the probability that a person who tested positive has the disease,
if 1% of people have the disease? - ANSWER - 40%
In this case, we know the following:
P(disease) = 0.01 (1%)
Therefore, P(no disease) = 0.99 (1-1%)
P(+ve result | disease) = 1 (since the test does not test negative if the
person has the disease)
P(+ve result | no disease) = 0.015 (since the test gives a positive result
for 1.5% of people who do not have the disease)
pg. 4
NEWEST 2026 TEST BANK| C960 DISCRETE
MATHEMATICS II OA EXAM REVIEW WITH
COMPLETE REAL EXAM QUESTIONS AND CORRECT
VERIFIED ANSWERS/ GRADED A+ (MOST RECENT!!)
C960 DISCRETE MATH II OA V1.
There are two coins, one fair and one biased. The biased coin comes up
heads with a probability 0.8 and tails with a probability 0.2. One of the
coins is selected at random and flipped ten times. The results of the coin
flips are mutually independent. The result of the 10 flips is H, T, T, H, H,
T, H, H, T, H.
What is the probability that the coin flipped was the biased coin? (Round
to the nearest tenth.) - ANSWER - 0.3 OR 30%
P(HHTTTHTHHT | B)=0.86 ×0.24
P(HHTTTHTHHT | F)=0.510
P(B)=P(F)=0.5
(0.8⁶ × 0.2⁴) × 0.5 / (0.8⁶ × 0.2⁴) × 0.5 + (0.5¹⁰) × 0.5
A life insurance company issues standard or preferred policies. Of the
company's policyholders, 60% have standard policies and a probability
of 0.01 of dying in the next year, and 40% have preferred policies and a
probability of 0.08 of dying in the next year. A policyholder dies in the
next year.
pg. 1
,What is the conditional probability of the deceased having a preferred
policy? - ANSWER - P(S) = 0.60, P(P) = 0.40,P(D|P) = 0.08, P(D|S) =
0.01, and the answer is 0.8421.
P(S)=0.60 (probability of having a standard policy)
P(P)=0.40 (probability of having a preferred policy)
P(D|P)=0.01 (probability of dying given a standard policy)
P(D|S)=0.08 (probability of dying given a preferred policy)
(0.08 × 0.40) / (0.08 × 0.40) + (0.60 ×0.01) = 0.8421
Which formula is the expected value of the random variable Y? -
ANSWER - (upper limit)∑(index = lower limit),
∑(s∈Y), | Y (s) | p(s)
There are four different colored balls in a bag. There is equal probability
of selecting the red, black, green, or blue ball. What is the expected
value of getting a green ball out of 20 experiments with replacement? -
ANSWER - 5
20 × .25
A company has three active projects: Domino, Falcon, and Giant. There
are 19 employees charging time to Domino, 16 to Falcon, and 15 to
Giant. Those totals include 8 employees charging both Domino and
Falcon, 6 charging both Falcon and Giant, and 7 charging both Giant and
pg. 2
,Domino. Included in those subtotals is the 4-person IT team, all of
whose members charge all three projects.
How many employees are working on the projects? - ANSWER - 33
Total employee = 19 + 16 + 15 = 20
Charging employees = 8 + 7 + 6 = 21
Duplicate charges = 21 - 4 = 17
Actually working employees = 50 - 17 = 33
A random experiment consists of tossing a fair six-sided die repeatedly.
How many tosses are required to be certain that the probability that at
least one '6' appears is greater than or equal to 1/2? - ANSWER - 4
The probability of not getting a 6 in one toss is P(not 6)=56
Now, applying this value into the expression we found in step(1),
⇒1−(P(not 6))n≥1/2
⇒1−(5/6)n≥1/2
⇒−(5/6)n≥−1/2
⇒(5/6)n≤1/2
⇒ln(5/6)n≤ ln(12)
⇒n×ln(5/6)≤ ln(1/2)
⇒n≤ ln(1/2)ln(5/6) = 3.80 round to 4
pg. 3
, An encryption scheme uses the numerical position of a letter in the
alphabet to encrypt characters, e.g., A=1, D=4, Z=26, etc., and spaces
are ignored. What is the encoding of "HAPPY BIRTHDAY" using this
technique? - ANSWER - 8116162529182084125
An individual has chosen the public key of N = 187 = 11 x 17 and e = 3.
What is the private key using RSA encryption? - ANSWER - 107
To find the RSA private key d, you calculate the modular inverse of the
public exponent e with respect to (p−1)(q−1), where p and q are the
prime factors of N. Here, N=187 is factored into p=11 and q=17. Thus,
ϕ(N)=(11−1)(17−1)=160. The private key d satisfies 3d≡1mod160.
Using the Extended Euclidean Algorithm, we find d=107, which is the
modular inverse of 3 modulo 160.
Assume that a test for a disease gives a positive result for 1.5% of people
who do not have the disease, but does not test negative if the person has
the disease.
What is the probability that a person who tested positive has the disease,
if 1% of people have the disease? - ANSWER - 40%
In this case, we know the following:
P(disease) = 0.01 (1%)
Therefore, P(no disease) = 0.99 (1-1%)
P(+ve result | disease) = 1 (since the test does not test negative if the
person has the disease)
P(+ve result | no disease) = 0.015 (since the test gives a positive result
for 1.5% of people who do not have the disease)
pg. 4
