To calculate the probability that exactly 3 out of 4 households have cable TV, you can use the binomial probability formula:
P(X = k) = (n choose k) * (p^k) * (q^(n-k))
Where:
- P(X = k) is the probability of getting exactly k successes.
- n is the total number of trials (in this case, households).
- k is the number of successful trials (in this case, households with cable TV).
- p is the probability of success on a single trial.
- q is the probability of failure on a single trial (q = 1 - p).
In your case:
- n = 4 (total households).
- k = 3 (the number of households with cable TV).
- p is the probability that a household has cable TV.
- q is the probability that a household does not have cable TV (1 - p).
You'll need to know the value of p, the probability that a household has cable TV, to calculate the probability. Once you have that value, you can plug it into the formula to find the probability of exactly 3 out of 4 households having cable TV.