The probability that a new flashlight will last more than a year is 0.92. The probability that it will last more

The probability that a new flashlight will last more than a year is 0.92. The probability that it will last more than two years is 0.86. Find the probability that it will last less than two years, but more than a year.

Let A – flashlight last more than a year, but less than two years;
B – the flashlight will last more than two years;
C – the flashlight will last exactly two years;
then A + B + C – the flashlight 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 of these events. The probability of an event C, consisting in the fact that
the flashlight will fail exactly two years later – exactly on the same day, hour and second – 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 obtain
0.92 = P (A) + 0.86;
Thus, for the required probability we have:
P (A) = 0.92 – 0.86 = 0.06;
Answer: The probability that the flashlight will last less than two years, but more than a year is P (A) = 0.06;