6/8/25, 4:39 PM Graded Exam 2
Topic 4: Random Variables
Started on Sunday, June 8, 2025, 5:16 PM
State Finished
Completed on Sunday, June 8, 2025, 5:39 PM
Time taken 23 mins 2 secs
Grade 120.00 out of 125.00 (96%)
Question 1
Which of the following best defines an 'Outcome' in probability theory?
Correct
5.00 points out Select one:
of 5.00 a. An individual result of an experiment.
b. A planned operation carried out under controlled conditions.
c. The set of all possible results in a chance experiment.
d. A measure of certainty about the occurrence of an event.
Question 2
An event A has a probability of P(A)=0.5. Which statement best describes the likelihood of
Correct
event A occurring?
5.00 points out
of 5.00 Select one:
a. Event A is equally likely to occur or not occur.
b. Event A will definitely occur every time.
c. Event A is unlikely to occur.
d. Event A will never occur.
, 6/8/25, 4:39 PM Graded Exam 2
Question 3
Now, imagine you draw three cards from the same deck without replacing them after each draw.
Correct
You pick the King of Hearts, the Three of Diamonds, and the Jack of Spades. Since you are
15.00 points out sampling without replacement, you cannot draw the same card twice.
of 15.00
Based on the comprehension above, answer the following questions:
1. After drawing the first card, how many cards remain in the deck before the second draw?
49 cards
51 cards
52 cards
50 cards
2. What is the probability of drawing the King of Hearts first and the Three of Diamonds second without replacement?
1 1
+
52 51
1 1
×
52 51
2
103
1 1
×
52 52
3. Are the events of drawing the King of Hearts and then the Three of Diamonds independent?
No, because the first draw affects the probabilities of the second.
No, because you can draw the same card again.
Yes, because drawing one card doesn't affect the next.
Yes, because both events have the same probability.
Question 4
In a game of chance, a player rolls a six-sided die and flips a coin. What is the probability of rolling
Correct
a 4 and getting heads?
5.00 points out
of 5.00 Select one:
a. 1 + 1 = 2 1 +1 = 2
2
b. ( 12 )2 2 = 1
4
(21)2 = 1
c. 1 1 1
× =
d. ( 1 × 1 ) = 1 (1 × 1) = 1
Question 5
A lamp manufacturer finds that 5% of the lamps produced are defective. If a lamp is selected at
Correct
random, what is the probability that the lamp is not defective.
5.00 points out
of 5.00 Select one:
a. 1.00
b. 0.95
c. 0.50
d. 0.05
Topic 4: Random Variables
Started on Sunday, June 8, 2025, 5:16 PM
State Finished
Completed on Sunday, June 8, 2025, 5:39 PM
Time taken 23 mins 2 secs
Grade 120.00 out of 125.00 (96%)
Question 1
Which of the following best defines an 'Outcome' in probability theory?
Correct
5.00 points out Select one:
of 5.00 a. An individual result of an experiment.
b. A planned operation carried out under controlled conditions.
c. The set of all possible results in a chance experiment.
d. A measure of certainty about the occurrence of an event.
Question 2
An event A has a probability of P(A)=0.5. Which statement best describes the likelihood of
Correct
event A occurring?
5.00 points out
of 5.00 Select one:
a. Event A is equally likely to occur or not occur.
b. Event A will definitely occur every time.
c. Event A is unlikely to occur.
d. Event A will never occur.
, 6/8/25, 4:39 PM Graded Exam 2
Question 3
Now, imagine you draw three cards from the same deck without replacing them after each draw.
Correct
You pick the King of Hearts, the Three of Diamonds, and the Jack of Spades. Since you are
15.00 points out sampling without replacement, you cannot draw the same card twice.
of 15.00
Based on the comprehension above, answer the following questions:
1. After drawing the first card, how many cards remain in the deck before the second draw?
49 cards
51 cards
52 cards
50 cards
2. What is the probability of drawing the King of Hearts first and the Three of Diamonds second without replacement?
1 1
+
52 51
1 1
×
52 51
2
103
1 1
×
52 52
3. Are the events of drawing the King of Hearts and then the Three of Diamonds independent?
No, because the first draw affects the probabilities of the second.
No, because you can draw the same card again.
Yes, because drawing one card doesn't affect the next.
Yes, because both events have the same probability.
Question 4
In a game of chance, a player rolls a six-sided die and flips a coin. What is the probability of rolling
Correct
a 4 and getting heads?
5.00 points out
of 5.00 Select one:
a. 1 + 1 = 2 1 +1 = 2
2
b. ( 12 )2 2 = 1
4
(21)2 = 1
c. 1 1 1
× =
d. ( 1 × 1 ) = 1 (1 × 1) = 1
Question 5
A lamp manufacturer finds that 5% of the lamps produced are defective. If a lamp is selected at
Correct
random, what is the probability that the lamp is not defective.
5.00 points out
of 5.00 Select one:
a. 1.00
b. 0.95
c. 0.50
d. 0.05
