Final Answer:
The probability that none of the 5 homes have a big-screen TV is 0.32768, which corresponds to option (b) 0.32.
Step-by-step explanation:
To calculate the probability that none of the 5 homes have a big-screen TV, we need to consider the probability that each individual home does not have a big-screen TV and then multiply these probabilities together. Assuming the probability of a home not having a big-screen TV is 0.8 (as having one would be 1 - 0.2 = 0.8), the calculation is as follows:
{None of the 5 homes have a big-screen TV}) = 0.8^5 = 0.32768 ]
So, the correct answer is (0.32768), which corresponds to option (b) 0.32. This result makes sense as the probability of each home not having a big-screen TV is multiplied together for all five homes, leading to a lower overall probability.
In summary, the probability of none of the homes having a big-screen TV is calculated by multiplying the individual probabilities, and it is essential to understand the concept of probabilities multiplying in independent events. This mathematical approach allows us to determine the likelihood of a specific outcome based on the given conditions and assumptions.