MATH SOLVE

2 months ago

Q:
# Assume that for a particular tire brand, the probability of wearing out before 30,000 miles is 0.25. For someone who buys a set of iour of these tires, what is the probability that all will last at least 30,000 miles? You be a suitable model in this case.

Accepted Solution

A:

Answer:The probability that all will last at least 30,000 miles is 0.3164.Step-by-step explanation:Consider the provided information.For a particular tire brand, the probability of wearing out before 30,000 miles is 0.25. Someone who buys a set of four of these tires,That means the probability of not wearing out is 1-0.25 = 0.75Now use the binomial distribution formula.[tex]^nC_r (p^{n-r})(q^r)[/tex]Substitute p = 0.25, q=0.75, r=4 and n=4[tex]^4C_4 (0.25)^{4-4}(0.75)^4[/tex][tex]1 \times 0.75^4[/tex][tex]0.3164[/tex]The probability that all will last at least 30,000 miles is 0.3164.