1. Let Pr(A) = 50% and Pr(B) = 67%. To the nearest whole percentage point, what

Question

1. Let Pr(A) = 50% and Pr(B) = 67%. To the nearest whole percentage point, what is the minimum possible ‘overlap’ found between these two events? Make sure to include the percent symbol (%). If this value cannot be determined based on the information given, then type in CBD.

2. Let Pr(A) = 42% and Pr(B) = 74%. To the nearest whole percentage point, what is the maximum possible ‘overlap’ found between these two events? Make sure to include the percent symbol (%). If this value cannot be determined based on the information given, then type in CBD.

Explanation / Answer

1)

here as we klnow that probability of an event can n ot be more than 100%

hence P(A U B) <=100%

P(A)+P(B)-P(A n B) <=100%

50%+67%-P(A n B) <=100%

P(A nB) > =17%

hence minium overlap =17%

2)

for overlap can not be higher than individual event probabilities

hence P(A n B) <=min( P(A) ; P(B))

P(A nB) <=min(42% ,74%)

P(A nB) <= 42%

therefore maximum overlap =42%

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.