Questions: A recent survey that 85% of a population watches TV at least once a day, 35% of the population uses a computer at least once a day, and 25% of the population do both. What is the probability that a person chosen at random from the population watches TV at least once a day or uses a computer at least once a day?

A recent survey that 85% of a population watches TV at least once a day, 35% of the population uses a computer at least once a day, and 25% of the population do both.
What is the probability that a person chosen at random from the population watches TV at least once a day or uses a computer at least once a day?
Transcript text: A recent survey that 85% of a population watches TV at least once a day, 35% of the population uses a computer at least once a day, and 25% of the population do both. What is the probability that a person chosen at random from the population watches TV at least once a day or uses a computer at least once a day?
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Solution

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Solution Steps

Step 1: Define the Events

Let A A be the event that a person watches TV at least once a day, and let B B be the event that a person uses a computer at least once a day. We are given the following probabilities:

  • P(A)=0.85 P(A) = 0.85
  • P(B)=0.35 P(B) = 0.35
  • P(AB)=0.25 P(A \cap B) = 0.25
Step 2: Use the Formula for the Union of Two Events

We need to find the probability that a person watches TV at least once a day or uses a computer at least once a day, which is the probability of the union of events A A and B B , denoted as P(AB) P(A \cup B) .

The formula for the probability of the union of two events is:

P(AB)=P(A)+P(B)P(AB) P(A \cup B) = P(A) + P(B) - P(A \cap B)

Step 3: Substitute the Given Probabilities

Substitute the given probabilities into the formula:

P(AB)=0.85+0.350.25 P(A \cup B) = 0.85 + 0.35 - 0.25

Step 4: Calculate the Probability

Calculate the probability:

P(AB)=0.85+0.350.25=0.95 P(A \cup B) = 0.85 + 0.35 - 0.25 = 0.95

Final Answer

The probability that a person chosen at random from the population watches TV at least once a day or uses a computer at least once a day is 0.95\boxed{0.95}.

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