Result
Probability of A NOT occuring: P(A') 0.5
Probability of B NOT occuring: P(B') 0.6
Probability of A and B both occuring: P(A∩B) 0.2
Probability that A or B or both occur: P(A∪B) 0.7
Probability that A or B occurs but NOT both: P(AΔB) 0.5
Probability of neither A nor B occuring: P((A∪B)') 0.3
Probability of A occuring but NOT B: 0.3
Probability of B occuring but NOT A: 0.2

Probability

Probability of A: P(A) = 0.5

Probability of B: P(B) = 0.4

Probability of A NOT occuring: P(A') = 1 - P(A) = 0.5

Probability of B NOT occuring: P(B') = 1 - P(B) = 0.6

Probability of A and B both occuring: P(A∩B) = P(A) × P(B) = 0.2

Probability that A or B or both occur: P(A∪B) = P(A) + P(B) - P(A∩B) = 0.7

Probability that A or B occurs but NOT both: P(AΔB) = P(A) + P(B) - 2P(A∩B) = 0.5

Probability of neither A nor B occuring: P((A∪B)') = 1 - P(A∪B) = 0.3

Probability of A occuring but NOT B: P(A) × (1 - P(B)) = 0.3

Probability of B occuring but NOT A: (1 - P(A)) × P(B) = 0.2

Probability

Probability of A occuring 5 time(s) = 0.65 = 0.07776

Probability of A NOT occuring = (1-0.6)5 = 0.01024

Probability of A occuring = 1-(1-0.6)5 = 0.98976

Probability of B occuring 3 time(s) = 0.33 = 0.027

Probability of B NOT occuring = (1-0.3)3 = 0.343

Probability of B occuring = 1-(1-0.3)3 = 0.657

Probability of A occuring 5 time(s) and B occuring 3 time(s) = 0.65 × 0.33 = 0.00209952

Probability of neither A nor B occuring = (1-0.6)5 × (1-0.3)3 = 0.00351232

Probability of both A and B occuring = (1-(1-0.6)5) × (1-(1-0.3)3) = 0.65027232

Probability of A occuring 5 times but not B = 0.65 × (1-0.3)3 = 0.02667168

Probability of B occuring 3 times but not A = (1-0.6)5 × 0.33 = 2.7648e-4

Probability of A occuring but not B = (1-(1-0.6)5) × (1-0.3)3 = 0.33948768

Probability of B occuring but not A = (1-0.6)5 × (1-(1-0.3)3) = 0.00672768

Probability

The probability between -1 and 1 is 0.68268

The probability outside of -1 and 1 is 0.31732

The probability of -1 or less (≤-1) is 0.15866

The probability of 1 or more (≥1) is 0.15866

CONFIDENCE INTERVALS TABLE
CONFIDENCE RANGE N
0.6828 -1.00000 – 1.00000 1
0.8 -1.28155 – 1.28155 1.281551565545
0.9 -1.64485 – 1.64485 1.644853626951
0.95 -1.95996 – 1.95996 1.959963984540
0.98 -2.32635 – 2.32635 2.326347874041
0.99 -2.57583 – 2.57583 2.575829303549
0.995 -2.80703 – 2.80703 2.807033768344
0.998 -3.09023 – 3.09023 3.090232306168
0.999 -3.29053 – 3.29053 3.290526731492
0.9999 -3.89059 – 3.89059 3.890591886413
0.99999 -4.41717 – 4.41717 4.417173413469

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