Worksheets — Set 17

Probability · Common distributions and limit theorems

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

Warm-up

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._

Written practice

1. P(A) = 1.1500000000000001, P(B) = 1.25. If independent, P(A∩B) = ___ 2. Binomial(n=22, p=0.5): P(X = 19) = ___ 3. E[X] for X with values {18, 20, 22} and equal probability ___ 4. Variance of a fair die roll: ___ 5. Conditional: P(A|B) when P(A∩B) = 0.44000000000000006 ___ 6. Identify the distribution and parameters in context. 7. P(A) = 1.3, P(B) = 1.4. If independent, P(A∩B) = ___ 8. Binomial(n=25, p=0.5): P(X = 22) = ___

___________________________ ___________________________ ___________________________ ___________________________

More written practice

1. E[X] for X with values {21, 23, 25} and equal probability ___ 2. Conditional: P(A|B) when P(A∩B) = 0.5 ___ 3. P(A) = 1.4500000000000002, P(B) = 1.5500000000000003. If independent, P(A∩B) = ___ 4. Binomial(n=28, p=0.5): P(X = 25) = ___ 5. E[X] for X with values {24, 26, 28} and equal probability ___ 6. Conditional: P(A|B) when P(A∩B) = 0.56 ___

___________________________ ___________________________ ___________________________ ___________________________ ___________________________

Patterns and rules

1. P(A) = 2, P(B) = 2.1. If independent, P(A∩B) = ___ 2. Binomial(n=39, p=0.5): P(X = 36) = ___ 3. E[X] for X with values {35, 37, 39} and equal probability ___

_See printable PDF for diagram._

___________________________ ___________________________ ___________________________ ___________________________

Stretch

1. P(A) = 2.4, P(B) = 2.5. If independent, P(A∩B) = ___ 2. Binomial(n=47, p=0.5): P(X = 44) = ___

___________________________ ___________________________ ___________________________ ___________________________

Parent tip: Draw a probability table or tree