Worksheets — Set 1

Probability · Random variables

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

Warm-up

1. P(A) = 0.4, P(B) = 0.5. If independent, P(A∩B) = ___ 2. Binomial(n=7, p=0.5): P(X = 4) = ___ 3. E[X] for X with values {3, 5, 7} and equal probability ___

_See printable PDF for diagram._

Written practice

1. P(A) = 0.35, P(B) = 0.45. If independent, P(A∩B) = ___ 2. Binomial(n=6, p=0.5): P(X = 3) = ___ 3. E[X] for X with values {2, 4, 6} and equal probability ___ 4. Variance of a fair die roll: ___ 5. Conditional: P(A|B) when P(A∩B) = 0.12000000000000001 ___ 6. Identify the distribution and parameters in context. 7. P(A) = 0.5, P(B) = 0.6000000000000001. If independent, P(A∩B) = ___ 8. Binomial(n=9, p=0.5): P(X = 6) = ___

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More written practice

1. E[X] for X with values {5, 7, 9} and equal probability ___ 2. Conditional: P(A|B) when P(A∩B) = 0.18 ___ 3. P(A) = 0.65, P(B) = 0.75. If independent, P(A∩B) = ___ 4. Binomial(n=12, p=0.5): P(X = 9) = ___ 5. E[X] for X with values {8, 10, 12} and equal probability ___ 6. Conditional: P(A|B) when P(A∩B) = 0.24000000000000002 ___

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Patterns and rules

1. P(A) = 1.2, P(B) = 1.3. If independent, P(A∩B) = ___ 2. Binomial(n=23, p=0.5): P(X = 20) = ___ 3. E[X] for X with values {19, 21, 23} and equal probability ___

_See printable PDF for diagram._

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Parent tip: Draw a probability table or tree