1.0 Points If P(A AND B) = 0, we say the two events A and B are independent. Tru
ID: 3219447 • Letter: 1
Question
1.0 Points
If P(A AND B) = 0, we say the two events A and B are independent.
True
False
1.0 Points
Which of the following pair of events would be the best example of two independent events?
A.A: it rains at 6 p.m. today. B: it rains at 6:05 p.m. today.
B.A: it snows today. B: it snows more than 2 inches today.
C.A: San Jose Sharks win Stanley Cup in 2014. B: Boston Bruins win Stanley Cup in 2014.
D.A: a die lands on 2. B: a coin lands on head.
1.0 Points
If two events are mutually exclusive, the probability that either event occurs is simply the sum of the individual probabilities.
True
False
1.0 Points
Saying that a set of events is collectively exhaustive implies that at least one of the events must occur.
True
False
1.0 Points
Assume I flip 3 fair coins. Let A denote the event that the middle coin is Heads. Let B denote the event that exactly 2 coins are Heads. What is the probability of the intersection of A and B. That is what is P(A AND B)? Please enter a decimal number between 0 and 1 with at least 2 significant digits
1.0 Points
When rolling two fair dice at the same time, what is the probability that the absolute difference between the two numbers landed is at most 1? Two examples of such an instance are (5, 5) and (1, 2). Please enter a decimal number between 0 and 1 with at least 2 significant digits .
1.0 Points
Consider a standard 52-card deck of cards. What is the probability of drawing either a seven or a black card?
1.0 Points
Suppose there are 3 biased coins. Each coin has probability 0.25 of landing on heads and probability 0.75 of landing on tails. 3 individuals flip the coins. If the coins do not all land on the same side, then the game ends. Otherwise, the players flip the coins again. What is the probability that the game ends at the first round?
1.0 Points
A route contains 2 intersections with traffic signals. The probability that one must stop at the first signal is 0.4. The probability that one must stop at the second signal is 0.5. The probability that one must stop at at least one of the two signals is 0.6. Compute the probability that one has to stop at exactly one signal.
1.0 Points
If two events A and B are independent and P(A) = 0.3 and P(B) = 0.6, compute P(A | B).
1.0 Points
Assume that you have an urn containing 10 balls of the following description:
4 are white (W) and lettered (L)
2 are white (W) and numbered (N)
3 are yellow (Y) and lettered (L)
1 is yellow (Y) and numbered (N)
If you draw a numbered ball (N), what is the probability that this ball is yellow (Y)?
1.0 Points
If P(A) = 0.4, P(B) = 0.3, and P(A | B) = 0.5, then compute P(A OR B).
1.0 Points
One box contains 6 red balls and 4 green balls, and a second box contains 7 red balls and 3 green balls. A ball is randomly chosen from the first box and placed in the second box. Then a ball is randomly selected from the second box and put in the first box. At the conclusion of this process what is the probability that the first box still contains 6 red balls and 4 green balls?
1.0 Points
Two cards are randomly selected without replacement from a deck of 52 cards. What is the probability the two cards constitute a pair, given that the two cards are different suits.
1.0 Points
A new steroid test is 85% effective in detecting a user when the individual has taken steroids. However, the test also yields a false-positive result for 2.0% of clean athletes tested. Suppose 70% of Olympics athletes are on steroids. If the test comes back negative, what is the probability the athlete is using steroids?
1.0 Points
If P(A AND B) = 0, we say the two events A and B are independent.
True
False
1.0 Points
Which of the following pair of events would be the best example of two independent events?
A.A: it rains at 6 p.m. today. B: it rains at 6:05 p.m. today.
B.A: it snows today. B: it snows more than 2 inches today.
C.A: San Jose Sharks win Stanley Cup in 2014. B: Boston Bruins win Stanley Cup in 2014.
D.A: a die lands on 2. B: a coin lands on head.
1.0 Points
If two events are mutually exclusive, the probability that either event occurs is simply the sum of the individual probabilities.
True
False
1.0 Points
Saying that a set of events is collectively exhaustive implies that at least one of the events must occur.
True
False
1.0 Points
Assume I flip 3 fair coins. Let A denote the event that the middle coin is Heads. Let B denote the event that exactly 2 coins are Heads. What is the probability of the intersection of A and B. That is what is P(A AND B)? Please enter a decimal number between 0 and 1 with at least 2 significant digits
1.0 Points
When rolling two fair dice at the same time, what is the probability that the absolute difference between the two numbers landed is at most 1? Two examples of such an instance are (5, 5) and (1, 2). Please enter a decimal number between 0 and 1 with at least 2 significant digits .
1.0 Points
Consider a standard 52-card deck of cards. What is the probability of drawing either a seven or a black card?
1.0 Points
Suppose there are 3 biased coins. Each coin has probability 0.25 of landing on heads and probability 0.75 of landing on tails. 3 individuals flip the coins. If the coins do not all land on the same side, then the game ends. Otherwise, the players flip the coins again. What is the probability that the game ends at the first round?
1.0 Points
A route contains 2 intersections with traffic signals. The probability that one must stop at the first signal is 0.4. The probability that one must stop at the second signal is 0.5. The probability that one must stop at at least one of the two signals is 0.6. Compute the probability that one has to stop at exactly one signal.
1.0 Points
If two events A and B are independent and P(A) = 0.3 and P(B) = 0.6, compute P(A | B).
1.0 Points
Assume that you have an urn containing 10 balls of the following description:
4 are white (W) and lettered (L)
2 are white (W) and numbered (N)
3 are yellow (Y) and lettered (L)
1 is yellow (Y) and numbered (N)
If you draw a numbered ball (N), what is the probability that this ball is yellow (Y)?
1.0 Points
If P(A) = 0.4, P(B) = 0.3, and P(A | B) = 0.5, then compute P(A OR B).
1.0 Points
One box contains 6 red balls and 4 green balls, and a second box contains 7 red balls and 3 green balls. A ball is randomly chosen from the first box and placed in the second box. Then a ball is randomly selected from the second box and put in the first box. At the conclusion of this process what is the probability that the first box still contains 6 red balls and 4 green balls?
1.0 Points
Two cards are randomly selected without replacement from a deck of 52 cards. What is the probability the two cards constitute a pair, given that the two cards are different suits.
1.0 Points
A new steroid test is 85% effective in detecting a user when the individual has taken steroids. However, the test also yields a false-positive result for 2.0% of clean athletes tested. Suppose 70% of Olympics athletes are on steroids. If the test comes back negative, what is the probability the athlete is using steroids?
Explanation / Answer
Q1) TRUE
Q 2 ) two events are said to be independent of each other, if the probability that one event occurs in no way affects the probability of occurence of another event.
Here A die lands on 2 and coin lands on Head are the best example of two independent events.
Option D ) is correct.
Q3 )True because Two events are mutually exclusive if they cannot occur at the same time.
Q 4 ) True.
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