A consumer organization estimates that 34% of the households in a particular community have one television set, 39% have 2 sets and 18% have three or more sets. If two households are chosen at random, what is the probability that at least one has a television set
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To find the probability that at least one household has a television set, we need to find the complement of the probability that neither household has a television set.
Let's calculate the probability that neither household has a television set first.
According to the information given:
- 34% of the households have one television set, which means that 66% (100% - 34%) of the households don't have one television set.
- Similarly, 39% of the households have two television sets, which means that 61% (100% - 39%) of the households don't have two television sets.
- And 18% of the households have three or more television sets, which means that 82% (100% - 18%) of the households don't have three or more television sets.
To find the probability that neither household has a television set, we multiply the probabilities of both households not having a television set. Since both households are chosen independently, we multiply the probabilities together.
Probability of neither household having a television set = (66% * 66%) = 0.4356
Now, let's find the probability that at least one household has a television set:
Probability of at least one household having a television set = 1 - Probability of neither household having a television set
Probability of at least one household having a television set = 1 - 0.4356
Probability of at least one household having a television set = 0.5644
So, the probability that at least one household has a television set is 0.5644 or 56.44%.