Worksheets — Set 12

Probability · Common distributions and limit theorems

Print and write your answers. Use diagrams to show thinking.

Warm-up

1. P(A) = 0.95, P(B) = 1.05. If independent, P(A∩B) = ___ 2. Binomial(n=18, p=0.5): P(X = 15) = ___ 3. E[X] for X with values {14, 16, 18} and equal probability ___

_See printable PDF for diagram._

Written practice

1. P(A) = 0.9000000000000001, P(B) = 1. If independent, P(A∩B) = ___ 2. Binomial(n=17, p=0.5): P(X = 14) = ___ 3. E[X] for X with values {13, 15, 17} and equal probability ___ 4. Variance of a fair die roll: ___ 5. Conditional: P(A|B) when P(A∩B) = 0.33999999999999997 ___ 6. Identify the distribution and parameters in context. 7. P(A) = 1.05, P(B) = 1.15. If independent, P(A∩B) = ___ 8. Binomial(n=20, p=0.5): P(X = 17) = ___

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More written practice

1. E[X] for X with values {16, 18, 20} and equal probability ___ 2. Conditional: P(A|B) when P(A∩B) = 0.4 ___ 3. P(A) = 1.2, P(B) = 1.3. If independent, P(A∩B) = ___ 4. Binomial(n=23, p=0.5): P(X = 20) = ___ 5. E[X] for X with values {19, 21, 23} and equal probability ___ 6. Conditional: P(A|B) when P(A∩B) = 0.45999999999999996 ___

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Patterns and rules

1. P(A) = 1.7500000000000002, P(B) = 1.85. If independent, P(A∩B) = ___ 2. Binomial(n=34, p=0.5): P(X = 31) = ___ 3. E[X] for X with values {30, 32, 34} and equal probability ___

_See printable PDF for diagram._

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Parent tip: Draw a probability table or tree