If ten households in this area are selected at random, what is the probability that exactly two of them will be in violation of this law?
To calculate the probability, we need to know two pieces of information:
1. The total number of households in this area.
2. The number of households in violation of this law in this area.
Without these details, we won't be able to provide an exact probability. However, I can explain the general steps to calculate this probability once you have the required information:
1. Determine the total number of households in the area.
2. Find out the number of households in violation of the law.
3. Use these values to calculate the probability of one household being in violation of the law.
- This can be done by dividing the number of households in violation by the total number of households.
4. Use the probability of one household being in violation to calculate the probability of two households being in violation out of ten.
- This can be done using the binomial probability formula:
P(X=k) = (nCk) * (p^k) * (q^(n-k))
where:
n = total number of trials or households (in this case, 10)
k = number of successful trials or households (in this case, 2)
p = probability of one household being in violation of the law
q = probability of one household not being in violation of the law (1 - p)
Once you have the required information, you can substitute the values into the formula to calculate the probability.