Statistics Questions

Q2 (201'). (a) Nine unmanned spacecraft are sent into space to observe the planet Mars. The probability of each spacecraft reaching Mars is independent of each other and is 12%. According to this, i. What is the probability that no spacecraft will reach Mars? ii. What is the probability that at least 1 spacecraft will reach Mars? iii. What is the probability that all spacecraft will reach Mars? (b) The number of false re alarms in a zone is 60 per month. According to the Poisson distribution, i. What is the probability that there will be no false re alarms on the next day? ii. What is the probability of having more than 2 false re alarms in the rst day to come? iii. What is the probability that at least 1 false re alarm will occur in the next 6 hours? iv. What is the probability that at most 1 false re alarm will occur in the next 8 hours