Question

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.

Answer 1

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 = 0.75

Now use the binomial distribution formula.

$^nC_r (p^{n-r})(q^r)$

Substitute p = 0.25, q=0.75, r=4 and n=4

$^4C_4 (0.25)^{4-4}(0.75)^4$

$1 \times 0.75^4$

$0.3164$

The probability that all will last at least 30,000 miles is 0.3164.