Worksheets — Set 20

Probability · Random variables

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

Warm-up

1. P(A) = 1.35, P(B) = 1.4500000000000002. If independent, P(A∩B) = ___ 2. Binomial(n=26, p=0.5): P(X = 23) = ___ 3. E[X] for X with values {22, 24, 26} and equal probability ___

_See printable PDF for diagram._

Written practice

1. P(A) = 1.3, P(B) = 1.4. If independent, P(A∩B) = ___ 2. Binomial(n=25, p=0.5): P(X = 22) = ___ 3. E[X] for X with values {21, 23, 25} and equal probability ___ 4. Variance of a fair die roll: ___ 5. Conditional: P(A|B) when P(A∩B) = 0.5 ___ 6. Identify the distribution and parameters in context. 7. P(A) = 1.4500000000000002, P(B) = 1.5500000000000003. If independent, P(A∩B) = ___ 8. Binomial(n=28, p=0.5): P(X = 25) = ___

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More written practice

1. E[X] for X with values {24, 26, 28} and equal probability ___ 2. Conditional: P(A|B) when P(A∩B) = 0.56 ___ 3. P(A) = 1.6, P(B) = 1.7000000000000002. If independent, P(A∩B) = ___ 4. Binomial(n=31, p=0.5): P(X = 28) = ___ 5. E[X] for X with values {27, 29, 31} and equal probability ___ 6. Conditional: P(A|B) when P(A∩B) = 0.62 ___

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Patterns and rules

1. P(A) = 2.15, P(B) = 2.25. If independent, P(A∩B) = ___ 2. Binomial(n=42, p=0.5): P(X = 39) = ___ 3. E[X] for X with values {38, 40, 42} and equal probability ___

_See printable PDF for diagram._

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Stretch

1. P(A) = 2.55, P(B) = 2.65. If independent, P(A∩B) = ___ 2. Binomial(n=50, p=0.5): P(X = 47) = ___

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Parent tip: Draw a probability table or tree