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Answer :
The probability that a theft can happen in a room that is left unlocked based on the statistics of dorm rooms affected by theft, is 1.89%
How to find the probability?
To find the probability that a room will be subjected to theft if it is left unlocked, the formula is:
= Probability that dorm room is left unlocked x Probability of dorm room being affected by theft x Probability that a theft occurs in a unlocked room
The probability of an unlocked room being robbed is therefore:
= 0.75 x 0.03 x 0.842
= 0.0225 x 0.842
= 0.018945
= 1.89%
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Final answer:
The probability of theft happening in a room, given that the room is unlocked, is calculated by multiplying the probability a room is left unlocked (0.75) by the conditional probability that a theft occurs in an unlocked room (0.842). This yields a probability of 0.631, or 63.1%.
Explanation:
The calculation of probability can be handled by considering each independent event separately then combining these probabilities. In this case, there are three events: the room is unlocked, a room is affected by theft, and thefts occur in unlocked rooms. First, the probability that a room is left unlocked is 0.75. Second, the probability that a room experiences a theft is 0.03. Third, given that a room has experienced a theft, it is 84.2% likely that it was left unlocked.
To find the probability of a theft occurring in an unlocked room, we multiply the probability of the room being unlocked by the probability that the theft occurs in an unlocked room. Hence, the probability of a theft occurring in an unlocked room is 0.75 * 0.842 = 0.631 (or 63.1%).
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