The probability of each tire on a car popping while driving

The probability of each tire on a car popping while driving is 0.7% within a 5-year time. 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. What is the probability that a tire will not pop in 5-years? Round to the nearest 100th of a percent. What is the probability that none of the tires pop in the next 5-years? Round to the nearest 100th of a percent. 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

P(each tire on a car popping while driving) = 0.7% = 0.007

a) Probability that the two back tires will pop in the next year

=> Probability of Popping one back tire * Probability of another back tire

[both the events are independent]

=> 0.007 * 0.007

=> 4.9 * 10^{-5}

In terms of percentage final answer will be 4.9 * E-3%

b) Probability that a tire will not pop in 5 years

=> (1 - tyre will pop out)

=> (1 - 0.007)

=> 0.993

Hence the correct answer is 99.3%

c) Probability that none of the tyre will pop out

=> (1-P(first pop out)) * (1-P(second pop out)) * (1-P(third pop out)) * (1-P(fourth pop out))

=> (0.993)^4

=> 0.9722926304

Hence nearest Percentage round off is equal to 97.23%

d) Probability that atleast one of the tyre will pop out

=> (1 - P(no tire will pop out))

=> (1 - 0.9722926304)

=> 0.0277073696

Hence answer in percentage is 2.77%