Cellular phones must be off during the class and test periods. They cannot these

Question

Cellular phones must be off during the class and test periods. They cannot these periods. Prairie View A&M; University is dedicated to a high standard of academic. students. In becoming part of the Prairie View A&M; University academic co for honesty and independent effort. Disciplinary action will be taken against others engages in any act of academic fraud or deceit. If P (A) = 0.75, P(B) = 0.85. and P(A or B) = 0.95. Are A and B independent, justify your answer. Find P (A|B), P( A' and B' ) P(A'|B)

Explanation / Answer

1.

i)

As

P(A n B) = P(A) + P(B) - P(A U B) = 0.75 + 0.85 - 0.95 = 0.65

Then

P(A|B) = P(A n B)/P(B) = 0.65/0.85 = 0.764705882

As P(A) =/= P(A|B), then THEY ARE NOT INDEPENDENT. [ANSWER]

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ii)

As

P(A n B) = P(A) + P(B) - P(A U B) = 0.75 + 0.85 - 0.95 = 0.65

Then

P(A|B) = P(A n B)/P(B) = 0.65/0.85 = 0.764705882 [ANSWER]

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iii)

P(A' n B') = 1 - P(A U B) = 1 - 0.95 = 0.05 [ANSWER]

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iv)

P(A'|B) = P(A' n B)/P(B) = [P(B) - P(A n B)]/P(B)

= (0.85 - 0.65)/0.85

= 0.235294118 [ANSWER]

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