A tire manufacturer advertises, "the median life of our new all-season radial tire is 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?

The probability that ALL tires will wear out before traveling 50,000 miles =

the probability that 1st tire will wear out before travelling 50000 miles x

the probability that 2nd tire will wear out before travelling 50000 miles x

the probability that 3rd tire will wear out before travelling 50000 miles x

the probability that 4th tire will wear out before travelling 50000 miles

Now, we need to get this probability:

P (A) = Number of favorable outcomes to A / Total number of outcomes

For this tire, we have only TWO possible outcomes:

Either the tire will travel 50000 miles, or

the tire will wear out before travelling 50000 miles

Therefore,

probability that a tire wears out before travelling 50000 miles = 1/2

Since the four tires are identical and they all have the same 2 options only, therefore:

probability that 1st tire wears out before 50000 miles =

probability that 2nd tire wears out before 50000 miles =

probability that 3rd tire wears out before 50000 miles =

probability that 4th tire wears out before 50000 miles

= 1/2

Substituting with this value in the first mentioned equation, we get:

probability that 4 tires wear out before travelling 50000 miles =

(1/2) x (1/2) x (1/2) x (1/2) = 1/16 = 0.0625