Question

4. Given that \( \mathrm{P}(A)=0.35, \mathrm{P}(B)=0.45 \) and \( \mathrm{P}(A \cap B)=0.13 \), (a) find \( \mathrm{P}\left(A^{\prime} \mid B^{\prime}\right) \), (2) (b) explain why the events \( A \) and \( B \) are not independent. (1) The event \( C \) has \( \mathrm{P}(C)=0.20 \). The events \( A \) and \( C \) are mutually exclusive and the events \( B \) and \( C \) are statistically independent. (c) Draw a Venn diagram to illustrate the events \( A, B \) and \( C \), giving the probabilities for each region. (d) Find \( \mathrm{P}\left([B \cup C]^{\prime}\right) \) (2) (Total for Question 4 is 10 marks)

          4. Given that \( \mathrm{P}(A)=0.35, \mathrm{P}(B)=0.45 \) and \( \mathrm{P}(A \cap B)=0.13 \),
(a) find \( \mathrm{P}\left(A^{\prime} \mid B^{\prime}\right) \),
(2)
(b) explain why the events \( A \) and \( B \) are not independent.
(1)

The event \( C \) has \( \mathrm{P}(C)=0.20 \).
The events \( A \) and \( C \) are mutually exclusive and the events \( B \) and \( C \) are statistically independent.
(c) Draw a Venn diagram to illustrate the events \( A, B \) and \( C \), giving the probabilities for each region.
(d) Find \( \mathrm{P}\left([B \cup C]^{\prime}\right) \)
(2)
(Total for Question 4 is 10 marks)

4. Given that P(A)=0.35, P(B)=0.45 and P(A ∩ B)=0.13,
(a) find P(A^'| B^'),
(2)
(b) explain why the events A and B are not independent.
(1)

The event C has P(C)=0.20.
The events A and C are mutually exclusive and the events B and C are statistically independent.
(c) Draw a Venn diagram to illustrate the events A, B and C, giving the probabilities for each region.
(d) Find P([B ∪ C]^')
(2)
(Total for Question 4 is 10 marks)

Added by John D.

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