Worksheets — Set 14

Probability · Common distributions and limit theorems

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

Warm-up

1. P(A) = 1.05, P(B) = 1.15. If independent, P(A∩B) = ___ 2. Binomial(n=20, p=0.5): P(X = 17) = ___ 3. E[X] for X with values {16, 18, 20} and equal probability ___

_See printable PDF for diagram._

Written practice

1. P(A) = 1, P(B) = 1.1. If independent, P(A∩B) = ___ 2. Binomial(n=19, p=0.5): P(X = 16) = ___ 3. E[X] for X with values {15, 17, 19} and equal probability ___ 4. Variance of a fair die roll: ___ 5. Conditional: P(A|B) when P(A∩B) = 0.38 ___ 6. Identify the distribution and parameters in context. 7. P(A) = 1.1500000000000001, P(B) = 1.25. If independent, P(A∩B) = ___ 8. Binomial(n=22, p=0.5): P(X = 19) = ___

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More written practice

1. E[X] for X with values {18, 20, 22} and equal probability ___ 2. Conditional: P(A|B) when P(A∩B) = 0.44000000000000006 ___ 3. P(A) = 1.3, P(B) = 1.4. If independent, P(A∩B) = ___ 4. Binomial(n=25, p=0.5): P(X = 22) = ___ 5. E[X] for X with values {21, 23, 25} and equal probability ___ 6. Conditional: P(A|B) when P(A∩B) = 0.5 ___

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Patterns and rules

1. P(A) = 1.85, P(B) = 1.9500000000000002. If independent, P(A∩B) = ___ 2. Binomial(n=36, p=0.5): P(X = 33) = ___ 3. E[X] for X with values {32, 34, 36} and equal probability ___

_See printable PDF for diagram._

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Parent tip: Draw a probability table or tree