Question

В телевизоре 12 ламп. Каждая лампа работает независимо от остальных и не выходит из строя в течение года с вероятностью p. Какова вероятность того, что в течение года хотя бы одна лампа выйдет из строя?

Answer 1

Вероятность это отношение числа благоприятных событий(в данном случае 1), к числу всех возможных (12), то есть 1\12
думаю, что так 

Answer 2

Probability of a Lamp Failing

To calculate the probability of at least one lamp failing within a year, we can use the concept of complementary events. The probability of at least one lamp failing is equal to 1 minus the probability of no lamps failing.

The probability of a single lamp not failing within a year is given as p. Since each lamp operates independently, the probability of no lamps failing within a year is (1 - p) raised to the power of the number of lamps.

The formula for the probability of at least one lamp failing within a year is:

P(at least one lamp failing) = 1 - (1 - p)^n

Where: - p = probability of a single lamp not failing within a year - n = number of lamps (in this case, 12)

Using the provided information, we can calculate the probability.

The probability of at least one lamp failing within a year is 1 - (1 - p)^12.

Calculation

Given that the probability of a single lamp not failing within a year is p = 0.2, we can substitute this value into the formula:

P(at least one lamp failing) = 1 - (1 - 0.2)^12

Calculating this gives us the probability of at least one lamp failing within a year.

Result

The probability of at least one lamp failing within a year, based on the given information, is approximately 0.8915 or 89.15%.

This means that there is an approximately 89.15% chance that at least one lamp will fail within a year.

(#1)