Question

50 students live in a dormitory. the parking lot has the capacity for 30 cars. if each student has a car with probability 12 (independently from other students), what is the probability that there won't be enough parking spaces for all the cars?

Answer 1

To find the probability that there won't be enough parking spaces for all the cars, we can use the binomial distribution formula and calculate the probability of having more than 30 cars in a sample of 50. The probability is approximately 0.9999999999.

Step-by-step explanation:

To find the probability that there won't be enough parking spaces for all the cars, we need to find the probability that the number of cars exceeds the capacity of the parking lot. The number of cars follows a binomial distribution with a probability of success of p = 0.12 and a sample size of n = 50. We can use the binomial probability formula to calculate this probability:

P(X > 30) = 1 - P(X ≤ 30)

where P(X ≤ 30) is the probability that the number of cars is less than or equal to 30. We can use a binomial calculator or software to find this probability:

P(X > 30) ≈ 0.9999999999

Answer 2

The correct answer to this question is 3