Worksheets — Set 11

Probability · Common distributions and limit theorems

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

Warm-up

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 ___

_See printable PDF for diagram._

Written practice

1. P(A) = 0.8500000000000001, P(B) = 0.9500000000000001. If independent, P(A∩B) = ___ 2. Binomial(n=16, p=0.5): P(X = 13) = ___ 3. E[X] for X with values {12, 14, 16} and equal probability ___ 4. Variance of a fair die roll: ___ 5. Conditional: P(A|B) when P(A∩B) = 0.32 ___ 6. Identify the distribution and parameters in context. 7. P(A) = 1, P(B) = 1.1. If independent, P(A∩B) = ___ 8. Binomial(n=19, p=0.5): P(X = 16) = ___

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More written practice

1. E[X] for X with values {15, 17, 19} and equal probability ___ 2. Conditional: P(A|B) when P(A∩B) = 0.38 ___ 3. P(A) = 1.1500000000000001, P(B) = 1.25. If independent, P(A∩B) = ___ 4. Binomial(n=22, p=0.5): P(X = 19) = ___ 5. E[X] for X with values {18, 20, 22} and equal probability ___ 6. Conditional: P(A|B) when P(A∩B) = 0.44000000000000006 ___

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Patterns and rules

1. P(A) = 1.7000000000000002, P(B) = 1.8000000000000003. If independent, P(A∩B) = ___ 2. Binomial(n=33, p=0.5): P(X = 30) = ___ 3. E[X] for X with values {29, 31, 33} and equal probability ___

_See printable PDF for diagram._

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Parent tip: Draw a probability table or tree