Worksheets — Set 18

Probability · Random variables

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

Warm-up

1. P(A) = 1.25, P(B) = 1.35. If independent, P(A∩B) = ___ 2. Binomial(n=24, p=0.5): P(X = 21) = ___ 3. E[X] for X with values {20, 22, 24} and equal probability ___

_See printable PDF for diagram._

Written practice

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 ___ 4. Variance of a fair die roll: ___ 5. Conditional: P(A|B) when P(A∩B) = 0.45999999999999996 ___ 6. Identify the distribution and parameters in context. 7. P(A) = 1.35, P(B) = 1.4500000000000002. If independent, P(A∩B) = ___ 8. Binomial(n=26, p=0.5): P(X = 23) = ___

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More written practice

1. E[X] for X with values {22, 24, 26} and equal probability ___ 2. Conditional: P(A|B) when P(A∩B) = 0.52 ___ 3. P(A) = 1.5000000000000002, P(B) = 1.6. If independent, P(A∩B) = ___ 4. Binomial(n=29, p=0.5): P(X = 26) = ___ 5. E[X] for X with values {25, 27, 29} and equal probability ___ 6. Conditional: P(A|B) when P(A∩B) = 0.58 ___

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Patterns and rules

1. P(A) = 2.05, P(B) = 2.15. If independent, P(A∩B) = ___ 2. Binomial(n=40, p=0.5): P(X = 37) = ___ 3. E[X] for X with values {36, 38, 40} and equal probability ___

_See printable PDF for diagram._

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Stretch

1. P(A) = 2.4499999999999997, P(B) = 2.55. If independent, P(A∩B) = ___ 2. Binomial(n=48, p=0.5): P(X = 45) = ___

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Parent tip: Draw a probability table or tree