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
