What does OR mean for combined probabilities?

OR means add (+) and is used for mutually exclusive events to find the probability of one event or the other event occurring.

True or False? The sum of all probabilities is 1.

True. As long as the possibilities considered are all mutually exclusive (non-overlapping), then the sum of all probabilities is 1.

Define independent events .

Independent events are events where the outcome of one event does not affect the outcome of the other event(s).

Define mutually exclusive events .

Mutually exclusive events are events that cannot occur at the same time.

What is the assumption made when using the multiplication rule for combined probabilities?

The assumption made when using the multiplication rule for combined probabilities is that the events are independent.

What is the assumption made when using the addition rule for combined probabilities?

The assumption made when using the addition rule for combined probabilities is that the events are mutually exclusive.

True or False? Tree diagrams are required for all combined probability questions.

False. Tree diagrams are not required for all combined probability questions, and may not be necessary if the question can be solved more quickly without one.

What is conditional probability?

Conditional probability is the probability of an event occurring, given that another event has occurred.

True or False? Conditional probability is often used in the context of Venn diagrams, tree diagrams, or two-way tables.

True. Conditional probability is often used in the context of Venn diagrams, tree diagrams, or two-way tables.

What does the phrase "given that" typically indicate in a probability question?

The phrase "given that" typically indicates a conditional probability question.

State what "without replacement" means in the context of probability questions.

Without replacement refers to situations where an item is drawn from a group and not returned before another draw is made.

True or False? Conditional probability questions can be solved without drawing diagrams.

True. Conditional probability questions can be solved without drawing diagrams, although diagrams can often be helpful.

True or False? Conditional probability questions always use the phrase "given that".

False. Conditional probability questions do not always use the phrase "given that", and the question may need to be interpreted to identify the conditional aspect.

True or False? Conditional probability is only used in situations were things are drawn or selected without replacement.

False. Conditional probability is used in situations where things are drawn or selected without replacement. But it is also used in other situations where the outcome of one event affects the probabilities for another event occurring.

True or False? Combined conditional probability questions can involve using both the AND and OR rules from combined probability.

True. Combined conditional probability questions can involve using both the AND and OR rules from combined probability.

What rule is used for independent events in combined conditional probability?

The AND rule (multiplication) is used for independent events in combined conditional probability, to find the probability that the independent events all occur.

What rule is used for mutually exclusive events in combined conditional probability?

The OR rule (addition) is used for mutually exclusive events in combined conditional probability, to find the probability that one or another of the mutually exclusive events occurs.

True or False? In combined conditional probability questions, probabilities for subsequent events may change based on previous events.

True. In combined conditional probability questions, probabilities for subsequent events may change based on previous events.

What is the assumption made when using the multiplication rule for combined conditional probabilities?

The assumption made when using the multiplication rule for combined conditional probabilities is that the events are independent.

True or False? Combined conditional probability questions can involve events happening simultaneously, or one after the other in a specific order.

True. Combined conditional probability questions can involve events happening simultaneously, or one after the other in a specific order. However this does not change the mathematics of the question.

Why is it a good idea not to simplify any probability fractions until the very end of a question?

Probabilities will often need to be added together to get to the final answer. This is easiest to do when they have the same denominator.

IGCSEMaths A: HigherEdexcelFlashcards

Combined & Conditional Probability (Edexcel IGCSE Maths A)

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What does AND mean for combined probabilities?

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What does AND mean for combined probabilities?
AND means multiply ( $\times$ ) and is used for independent events to find the probability of both events occurring.
What does OR mean for combined probabilities?
OR means add (+) and is used for mutually exclusive events to find the probability of one event or the other event occurring.
True or False?
The sum of all probabilities is 1.
True.
As long as the possibilities considered are all mutually exclusive (non-overlapping), then the sum of all probabilities is 1.
Define independent events.
Independent events are events where the outcome of one event does not affect the outcome of the other event(s).
Define mutually exclusive events.
Mutually exclusive events are events that cannot occur at the same time.
State the equation for the probability of two independent events, $A$ and $B$ , occurring together.
If $A$ and $B$ are independent events, then the probability of both events occurring is
$P (A and B) = P (A) \times P (B)$
State the equation for the probability of one or the other of two mutually exclusive events, $A$ and $B$ , occurring.
If $A$ and $B$ are mutually exclusive events, then the probability of one or the other of them occurring is
$P (A or B) = P (A) + P (B)$
What is the assumption made when using the multiplication rule for combined probabilities?
The assumption made when using the multiplication rule for combined probabilities is that the events are independent.
What is the assumption made when using the addition rule for combined probabilities?
The assumption made when using the addition rule for combined probabilities is that the events are mutually exclusive.
True or False?
Tree diagrams are required for all combined probability questions.
False.
Tree diagrams are not required for all combined probability questions, and may not be necessary if the question can be solved more quickly without one.
What is conditional probability?
Conditional probability is the probability of an event occurring, given that another event has occurred.
What is the notation for the conditional probability of event $A$ occurring, given that event $B$ has occurred?
The notation for the conditional probability of event $A$ occurring, given that event $B$ has occurred, is $P (A | B)$ .
True or False?
Conditional probability is often used in the context of Venn diagrams, tree diagrams, or two-way tables.
True.
Conditional probability is often used in the context of Venn diagrams, tree diagrams, or two-way tables.
What does the phrase "given that" typically indicate in a probability question?
The phrase "given that" typically indicates a conditional probability question.
What might $P (passes | no revision)$ mean in the context of a student preparing for an exam?
$P (passes | no revision)$ would be the probability that the student passes the exam, given that the student has done no revision.
State what "without replacement" means in the context of probability questions.
Without replacement refers to situations where an item is drawn from a group and not returned before another draw is made.
True or False?
Conditional probability questions can be solved without drawing diagrams.
True.
Conditional probability questions can be solved without drawing diagrams, although diagrams can often be helpful.
True or False?
Conditional probability questions always use the phrase "given that".
False.
Conditional probability questions do not always use the phrase "given that", and the question may need to be interpreted to identify the conditional aspect.
What is the difference between $P (A | B)$ and $P (B | A)$ ?
The difference between $P (A | B)$ and $P (B | A)$ is this:
- $P (A | B)$ is the probability that $A$ happens, given that $B$ has happened
- $P (B | A)$ is the probability that $B$ happens, given that $A$ has happened
True or False?
Conditional probability is only used in situations were things are drawn or selected without replacement.
False.
Conditional probability is used in situations where things are drawn or selected without replacement.
But it is also used in other situations where the outcome of one event affects the probabilities for another event occurring.
True or False?
Combined conditional probability questions can involve using both the AND and OR rules from combined probability.
True.
Combined conditional probability questions can involve using both the AND and OR rules from combined probability.
What rule is used for independent events in combined conditional probability?
The AND rule (multiplication) is used for independent events in combined conditional probability, to find the probability that the independent events all occur.
What rule is used for mutually exclusive events in combined conditional probability?
The OR rule (addition) is used for mutually exclusive events in combined conditional probability, to find the probability that one or another of the mutually exclusive events occurs.
True or False?
In combined conditional probability questions, probabilities for subsequent events may change based on previous events.
True.
In combined conditional probability questions, probabilities for subsequent events may change based on previous events.
State the equation for the probability of two independent events, $A$ and $B$ , occurring together.
If $A$ and $B$ are independent events, then the probability of both events occurring is
$P (A and B) = P (A) \times P (B)$
State the equation for the probability of one or the other of two mutually exclusive events, $A$ and $B$ , occurring.
If $A$ and $B$ are mutually exclusive events, then the probability of one or the other of them occurring is
$P (A or B) = P (A) + P (B)$
What is the assumption made when using the multiplication rule for combined conditional probabilities?
The assumption made when using the multiplication rule for combined conditional probabilities is that the events are independent.
True or False?
Combined conditional probability questions can involve events happening simultaneously, or one after the other in a specific order.
True.
Combined conditional probability questions can involve events happening simultaneously, or one after the other in a specific order. However this does not change the mathematics of the question.
Why is it a good idea not to simplify any probability fractions until the very end of a question?
Probabilities will often need to be added together to get to the final answer. This is easiest to do when they have the same denominator.

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