The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B)
True
The probability of passing a test given attendance at all lectures is approximately 83%
True
Dependent events are characterized by conditional probabilities
The probability of passing a test given that all lectures were attended is approximately 0.83
In dependent events, P(A|B) is not equal to P(A).
True
What does conditional probability measure?
Probability of A given B
What is the meaning of P(A|B) in conditional probability?
Conditional probability of A given B
Independent events have probabilities that are influenced by each other.
False
In the example of passing a test and attending lectures, P(A ∩ B) represents the probability of passing and attending all lectures.
If there is a 60% chance of rain and an 80% chance the roads will be slippery if it rains, the probability that the roads are slippery given rain is 0.8.
True
Steps to construct a tree diagram
1️⃣ Identify the events and their probabilities
2️⃣ Draw branches for each possible outcome
3️⃣ Label probabilities on each branch
What three probabilities must be determined to use the conditional probability formula?
P(A), P(B), P(A ∩ B)
Conditional probability refers to the probability of an event A occurring, given that another event B has already occurred
In the formula for conditional probability, P(A|B) represents the probability of A given B
Independent events are events where the occurrence of one event affects the probability of the other
False
What is the probability of passing a test and attending all lectures simultaneously?
0.75
In independent events, P(A|B) is equal to P(A)
To apply the conditional probability formula, the joint probability of A and B is divided by the probability of B
The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B).
True
Dependent events affect each other's probabilities.
True
The outcome of rolling a die is independent of flipping a coin.
True
Steps to construct a tree diagram:
1️⃣ Identify the events and their probabilities
2️⃣ Draw branches for each possible outcome
3️⃣ Label the probabilities on each branch
4️⃣ Write conditional probabilities for second events
In a tree diagram for conditional probability, the probability of the second event is conditional on the first event.
True
Match the component of the conditional probability formula with its description:
P(A|B) ↔️ Conditional probability of A given B
P(A ∩ B) ↔️ Probability of both A and B occurring
P(B) ↔️ Probability of event B occurring
What is the probability of passing a test given that all lectures were attended, according to the example provided?
0.83
In the conditional probability formula, P(A ∩ B) represents the probability of both events A and B occurring
Steps to calculate conditional probability
1️⃣ Identify the events A and B
2️⃣ Find P(A ∩ B), the probability of both A and B occurring
3️⃣ Find P(B), the probability of B occurring
4️⃣ Apply the formula P(A|B) = P(A ∩ B) / P(B)
Match the component of the conditional probability formula with its meaning:
P(A|B) ↔️ Conditional probability of A given B
P(A ∩ B) ↔️ Probability of both A and B
P(B) ↔️ Probability of event B
Match the type of event with an example:
Dependent ↔️ Drawing cards without replacement
Independent ↔️ Flipping a coin and rolling a die
Steps to calculate P(A|B) using the given probabilities:
1️⃣ Identify P(A ∩ B)
2️⃣ Identify P(B)
3️⃣ Calculate P(A|B) using the formula
The conditional probability formula is written as P(A|B) = P(A ∩ B) / P(B)
The probability formula for dependent events is P(A|B) = P(A).
False
Tree diagrams are a visual tool for solving conditional probability problems.
When constructing a tree diagram, probabilities are labeled on each branch
P(A|B) represents the probability of event A occurring given that event B has already occurred.
True
In an example, 80% of students pass a test, 90% attend lectures, and 75% pass the test and attend all lectures. The probability of passing the test given attendance is approximately 83%
In the formula for conditional probability, P(A ∩ B) represents the probability of both A and B occurring
What is the conditional probability formula used in statistics?
P(A|B) = P(A ∩ B) / P(B)
What is an example of independent events?
Rolling a die and flipping a coin
The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B).