A survey of Mount Everest climbers in 2021 shows that 29 of those surveyed have successfully set foot on the summit a A random sample of 12 climbers was taken The number of climbers who successfully set foot on the summit can be modelled by a binomial distribution i State two assumptions made in order for this model to be valid ii Find the probability that at least four people from the sample made a successful summit climb b From a random sample of n climbers the probability that at least one of them made a successful summit climb in 2021 is greater than 0 995 Determine the least possible value of n 3 4