Assume that the monthly worldwide average number of airplaine crashes of commercial airlines is 2.22.2. What is the probability that there will be
(a) at most 44 such accidents in the next month?  
(b) more than 22 such accidents in the next 22 months?  
(c) exactly 88 such accidents in the next 44 months?

Assume that the monthly worldwide average number of airplane crashes of commercial airlines is 2.2. What is the probability that there will be
(a) more than 3 such accidents in the next month?
(b) at most 2 such accidents in the next 3 months?
(c) exactly 7 such accidents in the next 4 months?

3.5.18. A shirt manufacturer knows that, on the average, 2% of his product will not meet quality specifications. Find the greatest number of shirts constituting a lot that will have, with probability 0.95, fewer than five defectives.

Question is from a chapter on Central Limit Theorem and Chebyshev’s theorem.

Suppose the number of cars in a household has a binomial distribution
with parameters n = 9, and p = 25 %.
Find the probability of a household having:
(a) 0 or 2 cars
(b) 0 or fewer cars
(c) 4 or more cars
(d) fewer than 2 cars

You roll a six-faced dice and observe the number of dots on the top face.

(a) Specify the appropriate sample space S of the random experiment.

(b) Give an example of a partition of S. (Proof is unnecessary.)

(c) Give an example of a probability mass function (pmf) for S.

From a set of all eight-digit natural numbers, where only the digits from the set {0,1, 3, 5, 7, 9} are present in decimal notation. we draw one. Calculate the probability of the event that the sum of digits of the drawn number is equal to 3.

1. A is called a palindrome if it reads the same from left and right. For instance, 13631 is a
palindrome, while 435734 is not. A 6-digit number n is randomly chosen. Find the probability
of the event that
(a) n is a palindrome.
(b) n is odd and a palindrome.
(c) n is even and a palindrome.