Question: Otto's car has 2 headlights (left and right). The left headlight fails on average once every 12 months, but the right headlight fails on average

Otto's car has 2 headlights (left and right). The left headlight fails on average once every 12 months, but the right headlight fails on average once every 4 months due to a persistent error. Headlights fail independently of each other and the past. When a headlight fails, it is repaired instantly.

(a) What is the average time between any headlight failures?

(b) What is the probability that the right headlight fails next?

(c) Calculate the probability that both headlights work throughout the entire winter without failure (winter is 3 months).

(d) Calculate the probability that during the winter, all failures occur on the right headlight.

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