A real estate man has eight master keys to open several new homes. Only in master key will open any given hour. If 40% of these homes are usually left

Question

A real estate man has eight master keys to open several new homes. Only in master key will open any given hour. If 40% of these homes are usually left

A real estate man has eight master keys to open several new homes. Only in master key will open any given hour. If 40% of these homes are usually left unlocked, what is the probability that the real estate man can get into a specific home if he selects three master keys at random before leaving the office?

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - `5//8`
Let `A_(1) and A_(2)` be the events that the specific home is left unlicked, and is left locked, respectively. Then `P(A_(1))=0.4P(A_(2))=0.6.`
Let A be the evetn that the real estate man get into the specific home. Then
`P(A//A_(1))=1,P(A//A_(2))=(""^(7)C_(2))/(""^(8)C_(3))=3/8`
`impliesP(A)=P(A_(1))P(A//A_(2))+P(A_(2))(A//A_(2))`
`=(0.4)(1)+(0.6)(3//8)=4/10+18/80=5/8`