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The probability that a house in an urban area will be burglarized is 1%. If 20 houses are randomly selected, what is the probability that less than 2 of the houses will be burglarized?

A. 0.01
B. 0.99
C. 0.019
D. 0.981

User Technext
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1 Answer

2 votes

Final answer:

To find the probability that less than 2 out of 20 houses will be burglarized when the probability of burglary is 1%, we use the binomial probability formula for 0 and 1 burglaries and sum them. The resulting probability is approximately 0.981, which corresponds to answer choice D.

Step-by-step explanation:

The probability that a house in an urban area will be burglarized is 1%. Using the binomial probability formula, we can calculate the probability that less than 2 of the 20 houses selected at random will be burglarized. The binomial probability formula is:

P(X = x) = C(n, x) * p^x * (1 - p)^(n - x)

Where:

  • C(n, x) is the combination of n items taken x at a time.
  • p is the probability of a house being burglarized.
  • n is the number of trials or houses.
  • x is the number of successes or burglaries.

For less than 2 houses, we calculate the probability for 0 and 1 house being burglarized and sum them:

P(X < 2) = P(X = 0) + P(X = 1)

We can find:

  • P(X = 0) by setting x = 0
  • P(X = 1) by setting x = 1

After computing the probabilities and adding them, we get P(X < 2) which is very close to 0.981. Therefore, the correct answer is D. 0.981.

User Glazed
by
7.8k points
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