The room is illuminated by a lantern with two lamps. The probability of burning out one lamp is 0.3.

The room is illuminated by a lantern with two lamps. The probability of burning out one lamp is 0.3. Find the probability that at least one lamp will not burn out within a year.

Incompatible events (probability of burnout – 0.3; probability of operability – 0.7)

The probability of inconsistent positive events (at least one lamp will not burn out):

– both lamps did not burn out: P1 = 0.7 * 0.7 = 0.49.

– the first lamp is burned out, the second is not: P2 = 0.3 * 0.7 = 0.21.

– the first lamp did not burn out, the second burned out: P3 = 0.7 * 0.3 = 0.21.

P = P1 + P2 + P3 = 0.49 + 0.21 + 0.21 = 0.91 or 91%.

Check: P4 (both lamps burned out) = 0.3 * 0.3 = 0.09.

P + P4 = 0.91 + 0.09 = 1.