The probability that a new vacuum cleaner will last more than a year is 0.96. the probability that it will

The probability that a new vacuum cleaner will last more than a year is 0.96. the probability that it will last more than two years is 0.84. find the probability that it will last less than two years, but more than a year.

Let A – the vacuum cleaner last more than a year, but less than two years;
B – the vacuum cleaner will last more than two years;
C – the vacuum cleaner will last exactly two years;
then A + B + C – the vacuum cleaner will last more than a year;

Events A, B and C are inconsistent, the probability of their sum is equal to the sum of the probabilities
these events. The probability of event C, consisting in the fact that the vacuum cleaner will fail exactly two years later – exactly on the same day, hour and second – is equal to zero.
Then:

P (A + B + C) = P (A) + P (B) + P (C) = P (A) + P (B);

whence, using the data from the condition, we get:

0.96 = P (A) + 0.84;

Thus, for the required probability we have:

P (A) = 0.96 – 0.84 = 0.12;
Answer: The probability that the vacuum cleaner will last less than two years, but more
years P (A) = 0.12;