The probability of each tire on a car popping while driving

The probability of each tire on a car popping while driving is 0.26% within a 5-year time.

(1) What is the probability that the two back tires will pop in the next 5-years?

Write answers in Scientific Notation, for example 0.0000025% = 2.5E-6% (notice that it is negative 6). Be careful to change percent to a decimal before calculation and take the answer and change it back to a percent.

(2) What is the probability that a tire will not pop in 5-years? Round to the nearest 100th of a percent.

(3) What is the probability that none of the tires pop in the next 5-years? Round to the nearest 100th of a percent.

(4) What is the probability that at least one tire pops in the next 5-years? Round to the nearest 100th of a percent.

Hint: Use the previous answer.

Solution

1)

P(both will pop) = P(pop)^2 = 0.0026^2 = 0.00000676 0.000676% [answer]

2)

There are two ways that this can happen. Either the first one or the second tire will not pop up. Hence, we multiply the product of the probabilities by 2:

P(a tire will not pop) = 2 P(pop) P(not pop) = 2*0.0026*(1-0.0026) = 0.00518648 = 0.518648% [answer]

3)

P(none will pop) = P(not pop)^4 = (1-0.0026)^4 = 0.98964049 = 98.96% [answer]

4)

P(at least one will pop) = 1 - P(one will pop) = 1-0.98964049 = 0.01035951 = 1.036% [answer]