Worksheets — Set 7

Probability · Common distributions and limit theorems

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

Warm-up

1. P(A) = 0.7, P(B) = 0.8. If independent, P(A∩B) = ___ 2. Binomial(n=13, p=0.5): P(X = 10) = ___ 3. E[X] for X with values {9, 11, 13} and equal probability ___

_See printable PDF for diagram._

Written practice

1. P(A) = 0.65, P(B) = 0.75. If independent, P(A∩B) = ___ 2. Binomial(n=12, p=0.5): P(X = 9) = ___ 3. E[X] for X with values {8, 10, 12} and equal probability ___ 4. Variance of a fair die roll: ___ 5. Conditional: P(A|B) when P(A∩B) = 0.24000000000000002 ___ 6. Identify the distribution and parameters in context. 7. P(A) = 0.8, P(B) = 0.9. If independent, P(A∩B) = ___ 8. Binomial(n=15, p=0.5): P(X = 12) = ___

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More written practice

1. E[X] for X with values {11, 13, 15} and equal probability ___ 2. Conditional: P(A|B) when P(A∩B) = 0.30000000000000004 ___ 3. P(A) = 0.95, P(B) = 1.05. If independent, P(A∩B) = ___ 4. Binomial(n=18, p=0.5): P(X = 15) = ___ 5. E[X] for X with values {14, 16, 18} and equal probability ___ 6. Conditional: P(A|B) when P(A∩B) = 0.36 ___

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Patterns and rules

1. P(A) = 1.5000000000000002, P(B) = 1.6. If independent, P(A∩B) = ___ 2. Binomial(n=29, p=0.5): P(X = 26) = ___ 3. E[X] for X with values {25, 27, 29} and equal probability ___

_See printable PDF for diagram._

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Parent tip: Draw a probability table or tree