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ALL YOU NEED TO KNOW- WJEC STATISTICS 1
1. Simple Probability
Remember OR is + AND is ×
When 3 are selected from a group containing different types.
Example: If 2 red, 3 blue and 4 yellow, select 3.
C1 3 C1 4 C1
P(one of each colour) = 9
P(3 same colour) = P(3 blue) +P(3 yellow) = 9
C 2 7 C1
P(2 reds are selected) = 9
P(at least 1 yellow) = 1 P(no yellows) = 1- 9
3. Union and intersection (Venn diagram)
Union = A or B or both (total)
Intersection = Both A and B (overlap)
A/ is "not A"
P(AUB) = P(A)+P(B)-P(AB)
If mutually exclusive P(AB)=0
If independent P(AB) = P(A) × P(B)
Conditional probability: P(B|A) =P(AB)
4. Tree Diagrams
Will be given probability of one event dependent on another.
a) Find a probability by multiplying along branches and adding.
b) Will be conditional probability
c) A second item or test may be taken, draw a third set of branches.
d) Find probability that the second item gives a certain outcome, use
5. Discrete random variables
Usually given a table, but if given a formula make own table.
If probabilities given in terms of k, then use the total = 1 to find k.
Mean E(X) = xP(X=x)
E(X2) = x2 P(X=x)
Variance = E(X2) E(X)2 standard deviation = variance
E( ) P(X x)
If X1 and X2 are 2 independent occurrences find P(X1 + X2 = 4), find all
options of making total of 4 remember the order is important, 1-3, 2-2, 3-1.
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Combination of X
This topic will be the end of a variable or distribution question.
E(X), E(X2) and Var(X) will be given or already found in question.
E(3X-4) = 3E(X) 4 Var(3X-4) = 32Var(X)
E(5-2X) = 5 2E(X) Var(5-2X) = (-2)2Var(X)
E(6X2 +4X) = 6 E(X2)+4E(X)
7. Binomial Distribution
X~B(n,p) Mean E(X) = np Variance Var(X)=np(1-p)
If given mean and variance use simultaneous equations to find n and p.
Find probabilities using graphical calculator if the question states you can use