A tire manufacturer advertises that "one-half of our new all-season radial tire last at least 50,000 miles. An immediate adjustment will be made on any tire that does not last 50,000 miles." You purchased four of these tires. What is the probability that all four tires will wear out before traveling 50,000 miles?
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A. B. C. D. E.D
1/2*1/2*1/2*1/2 = 1/16 where 1/2 is the probability that a tire will wear our before 50,000 miles.
To solve this problem, we can assume that the probability of each tire wearing out before traveling 50,000 miles is 1/2, based on the information provided by the tire manufacturer.
Since there are four tires in total, we can calculate the probability of all four tires wearing out before reaching 50,000 miles by multiplying the probabilities of each individual tire wearing out.
The probability of the first tire wearing out before 50,000 miles is 1/2.
Given that the first tire has worn out before 50,000 miles, the probability of the second tire wearing out before 50,000 miles is also 1/2.
Similarly, for the third tire, the probability of it wearing out before 50,000 miles, given that the first two tires have worn out, is again 1/2.
Lastly, for the fourth tire, the probability of it wearing out before 50,000 miles, given that the first three tires have worn out, is also 1/2.
To calculate the overall probability, we multiply these individual probabilities together:
Probability = (1/2) * (1/2) * (1/2) * (1/2) = 1/16 or 0.0625
Therefore, the probability that all four tires will wear out before traveling 50,000 miles is 1/16 or 0.0625.
The correct answer is D. 1/16, or 0.0625.