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 a conditional probability .

A conditional probability is the probability of one thing happening given that something else has already happened. It is the words 'given that' which make a probability conditional.

What changes when a probability is conditional?

It is worked out from a smaller, restricted set of outcomes rather than from all of them. The condition tells you which outcomes to discard before you start counting.

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.

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. E.g. if there are a number of yellow sweets and green sweets in a jar and two sweets are eaten, the probability of picking a yellow sweet will be different for the first and second picks. This is because there will be fewer sweets, and different numbers of each kind of sweet, after the first is picked.

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 all have the same denominator .

IGCSEMathsEdexcelMaths BFlashcardsStatistics & ProbabilityCombined & Conditional Probability

Combined & Conditional Probability (Edexcel IGCSE Maths B): Flashcards

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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.
E.g. the probability of events A and B occurring is $P (A) \times P (B)$ .
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.
E.g. the probability of either event A and/or event B occurring is $P (A) + P (B)$ .
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.
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:
$P (A or B) = P (A) + P (B)$ .
Define a conditional probability.
A conditional probability is the probability of one thing happening given that something else has already happened.
It is the words 'given that' which make a probability conditional.
What changes when a probability is conditional?
It is worked out from a smaller, restricted set of outcomes rather than from all of them.
The condition tells you which outcomes to discard before you start counting.
A digit is chosen at random from 1 to 9. What is the probability that it is a multiple of 3?
It is $\frac{3}{9}$ , because 3, 6 and 9 are the multiples of 3 among all nine digits.
This is not a conditional probability, since nothing has restricted which digits are possible.
A digit is chosen at random from 1 to 9, given that it is even. What is the probability that it is a multiple of 3?
It is $\frac{1}{4}$ , because only 2, 4, 6 and 8 are now possible and just one of them, 6, is a multiple of 3.
The condition shrank the denominator from 9 to 4, and that is exactly what makes the probability conditional.
True or False?
A condition can make a probability larger than it was without the condition.
True.
Restricting the outcomes can leave the favourable ones as a bigger share of what remains.
Choosing a multiple of 3 from the digits 1 to 9 has probability $\frac{3}{9}$ , but among the odd digits 1, 3, 5, 7 and 9 it rises to $\frac{2}{5}$ .
Of 105 people who play tennis, 42 also play squash. What is the probability that a tennis player chosen at random also plays squash?
It is $\frac{42}{105} = \frac{2}{5}$ , because the condition restricts you to the 105 tennis players.
The 42 are counted out of that restricted group, not out of everyone who was surveyed.
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.
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.
E.g. if there are a number of yellow sweets and green sweets in a jar and two sweets are eaten, the probability of picking a yellow sweet will be different for the first and second picks.
This is because there will be fewer sweets, and different numbers of each kind of sweet, after the first is picked.
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 all have the same denominator.

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