The probability scale, mutually exclusive and independent events, tree diagrams, Venn diagrams, expected frequency and relative frequency.
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1.What is the range of the probability scale?
From 0, meaning impossible, to 1, meaning certain.
2.What do all the probabilities of an event add up to?
1
3.How do you find the probability of an event not happening?
Subtract the probability that it does happen from 1.
4.The probability of rain is 0.3. What is the probability of no rain?
1 minus 0.3 = 0.7.
5.What does mutually exclusive mean?
Two events that cannot both happen at the same time.
6.How do you find the probability of one event or another, if they are mutually exclusive?
Add the probabilities.
7.What does independent mean?
The outcome of one event does not affect the outcome of the other.
8.How do you find the probability of two independent events both happening?
Multiply the probabilities.
9.What is the probability of two heads when flipping two coins?
One half x one half = one quarter.
10.What is theoretical probability?
The probability worked out from the number of equally likely outcomes.
11.What is relative frequency?
Probability estimated from experimental results: the number of times an outcome occurred divided by the total number of trials.
12.How can relative frequency be made more reliable?
By carrying out more trials.
13.How do you find the expected frequency?
Multiply the probability by the number of trials.
14.A dice is rolled 300 times. How many sixes would you expect?
One sixth x 300 = 50.
15.Why might the actual number differ from the expected number?
Probability describes the long run pattern. Individual results vary by chance.
16.What is a sample space?
A list or table of all the possible outcomes of an event.
17.What do the branches at each stage of a tree diagram add up to?
1
18.How do you find a probability along a path in a tree diagram?
Multiply along the branches.
19.How do you combine several paths in a tree diagram?
Multiply along each path, then add the results together.
20.What does without replacement mean?
The item is not put back, so the total and the number of that item change for the second pick.
21.Ten counters include 4 red. Two are taken without replacement. What is the probability both are red?
4 over 10 x 3 over 9 = 12 over 90, which simplifies to 2 over 15.
22.Why does the second fraction change without replacement?
One counter has been removed, so both the number of red counters and the total are one smaller.
23.What does a Venn diagram show?
How sets of outcomes overlap, with the intersection showing outcomes in both sets.
24.What does the intersection of two sets mean?
The outcomes that belong to both sets at once.
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