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?
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?
Solution
Solution Steps
Step 1: Define the Events
Let A be the event that a person watches TV at least once a day, and let 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(B)=0.35
P(A∩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 and B, denoted as P(A∪B).
The formula for the probability of the union of two events is:
P(A∪B)=P(A)+P(B)−P(A∩B)
Step 3: Substitute the Given Probabilities
Substitute the given probabilities into the formula:
P(A∪B)=0.85+0.35−0.25
Step 4: Calculate the Probability
Calculate the probability:
P(A∪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.