Page 39 - Pra U STPM 2022 Penggal 3 - Maths (T)

Mathematics Semester 3 STPM Chapter 2 Probability

Summary

1. Addition principle of counting:
Let A , A , … A be disjoint events with n , n , … n possible outcomes, respectively.
2
1
2
k
k
1
Then the total number of outcomes for the event “A or A or … or A ” is n + n + … + n .
1 2 k 1 2 k
2. Multiplication principle of counting:
Let A , A , …, A be events with n , n , …, n possible outcomes, respectively.
2
2
1
k
k
1
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Then the total number of outcomes for the sequence of these k events is
n × n × … × n
1 2 k
3. First permutation rule 2

The number of permutation of n distinct elements is n!.
4. Second permutation rule
n!
The number of permutations of n distinct elements taken r at a time is, P = (n – r)! .
n
r
5. The number of distinct permutations of n elements of which n are of one kind, n of a second kind,
2
1
n!
…, n of a kth kind is given by the formula n ! n ! … n ! .
k
2
k
1
6. The number of possible combinations of choosing r elements from a set of n elements without regard
n!
n
to order is, C = (n – r)! r! .
r
7. An outcome is a result of some activity.
For example: Rolling a dice has six outcomes: 1, 2, 3, 4, 5, 6
8. In statistics the word experiment is used to describe any process that generates raw data or outcome.
9. A sample space is a set of all possible outcomes for an activity and is represented by S.
For example: The sample space for rolling a dice is, S = {1, 2, 3, 4, 5, 6}.
10. An event is the collection of outcomes of particular interest in an experiment.
11. An event is the subset of the sample space S.
12. Probability is a measure of how likely an event is to happen.
P(Event) = number of ways that an event can occur
total number of possible outcomes
13. (a) The probability that an event will happen is between 0 and 1 inclusive, i.e.
0 < P(E) < 1
(b) P(φ) = 0; φ is 0 collections.
(c) P(S) = 1

14. If an experiment can result in any one of N different equally likely outcomes, and if exactly n of these
outcomes correspond to event E, then the probability of event E is P(E) = n .
N

15. If an experiment is repeated n times under the identical condition and an event is observed to happen
f times, the probability of the event happening is then estimated to be
frequency of the event occured f
P(E) = =
total number of observations n

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02 STPM Math(T) T3.indd 107 28/10/2021 10:21 AM