Question

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One-fourth of the residents of a particular community leave their garage doors unlocked when they go out to do an errand. The local chief of police estimates that 5 percent of the garages with the doors unlocked will have something stolen, but only 1 percent of those locked will have something stolen. What is the probability if a garage is selected at random it will be unlocked? Express your answer as a decimal carried out two places, e.g .10.

One-fourth of the residents of a particular community leave their garage doors unlocked when they go out to do an errand. The local chief of police estimates that 5 percent of the garages with the doors unlocked will have something stolen, but only 1 percent of those locked will have something stolen. What is the probability if a garage is selected at random it will be locked? Express your answer as a decimal carried out two places, e.g .10.

One-fourth of the residents of a particular community leave their garage doors unlocked when they go out to do an errand. The local chief of police estimates that 5 percent of the garages with the doors unlocked will have something stolen, but only 1 percent of those locked will have something stolen. What is the probability if a garage that is unlocked is selected at random it will be robbed? Express your answer as a decimal carried out two places, e.g .10.

One-fourth of the residents of a particular community leave their garage doors unlocked when they go out to do an errand. The local chief of police estimates that 5 percent of the garages with the doors unlocked will have something stolen, but only 1 percent of those locked will have something stolen. What is the probability if a garage that is locked is selected at random it will be robbed? Express your answer as a decimal carried out two places, e.g .10.

One-fourth of the residents of a particular community leave their garage doors unlocked when they go out to do an errand. The local chief of police estimates that 5 percent of the garages with the doors unlocked will have something stolen, but only 1 percent of those locked will have something stolen. What is the probability if a garage is selected at random it will be unlocked and robbed? Express your answer as a decimal carried out four places, e.g .1234

One-fourth of the residents of a particular community leave their garage doors unlocked when they go out to do an errand. The local chief of police estimates that 5 percent of the garages with the doors unlocked will have something stolen, but only 1 percent of those locked will have something stolen. What is the probability if a garage is selected at random it will be locked and robbed? Express your answer as a decimal carried out four places, e.g .1234

One-fourth of the residents of a particular community leave their garage doors unlocked when they go out to do an errand. The local chief of police estimates that 5 percent of the garages with the doors unlocked will have something stolen, but only 1 percent of those locked will have something stolen. What is the probability if a garage is selected at random it will be robbed? Express your answer as a decimal carried out two places, e.g .12

One-fourth of the residents of a particular community leave their garage doors unlocked when they go out to do an errand. The local chief of police estimates that 5 percent of the garages with the doors unlocked will have something stolen, but only 1 percent of those locked will have something stolen. If a garaged is robbed , what is the probability the door was left unlocked? Express your answer as a decimal carried out three places, e.g .123

(It's broken down to 8 parts)

Thank you

Answer 1

1. One-fourth of the residents of a particular community leave their garage doors unlocked . This means if a garage is randomly selected, the probability that it will be unlocked is 1/4.

Let U be the event that a randomly selected garage's door is unlocked .

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ans: The probability if a garage is selected at random it will be unlocked is P(U)=0.25

2. Let L be the event that a randomly selected garage's door is locked. A door is either left locked or unlocked. Hence the sum of probability that a door is locked and probability that a door is unlocked is 1.

P(U)+P(L)=1.

Hence

ans: The probability if a garage is selected at random it will be locked is 0.75

3. Five percent of the garages with the doors unlocked will have something stolen. Let S be the event that something is stolen from a garage.

This is the conditional probability that something is stolen from the garage (event S) given that it is unlocked (event U)

ans: The probability if a garage that is unlocked is selected at random it will be robbed is 0.05

4. One percent of those locked will have something stolen. This is the conditional probability that something is stolen from the garage (event S) given that it is locked (event L)

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ans: The probability if a garage that is locked is selected at random it will be robbed 0.01

5.  the probability if a garage is selected at random it will be unlocked (event U) and robbed (event S) is

ans: the probability if a garage is selected at random it will be unlocked and robbed is 0.0125

6. the probability if a garage is selected at random it will be locked (event L) and robbed (event S) is

ans: the probability if a garage is selected at random it will be locked and robbed is 0.0075

7. the probability if a garage is selected at random it will be robbed (event S) is

ans: the probability if a garage is selected at random it will be robbed is 0.02

8. If a garaged is robbed (event S), what is the probability the door was left unlocked (Event U) is same as the conditional probability that the door was left unlocked given that the garage is robbed.

ans: If a garaged is robbed , what is the probability the door was left unlocked is 0.625