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.