Planet X has 155 calendar days. What is the probability that in a room with 14 inhabitants of Planet X that at least two of them share a birthday? You may assume that all 155 birthdays are equally likely among inhabitants of Planet X. Hint: Instead, find the probability that this does not happen by counting: • How many outcomes are in the sample space? That is, how many ways would there be to assign one of 155 birthdays to each of those 14 inhabitants, where repetition of birthdays is possible? • How many outcomes are in the event of interest (where no two people share a birthday)? That is, how many ways would there be to assign the 14 inhabitants different birthdays from among the 155 birthdays? Use this information to compute a precise probability. Input your answer as a percentage, i.e. a number between O meaning impossible and 100 meaning a certainty. Round your percentage to four decimal places. For example, for≈ 16.6667%, you would input 16.6667.

a bookstore owner examines 6 books from each lot of 20 to check for missing pages.If he finds at least 3 books with missing pages, the entire lot is returned Mean- Probability

Assume that when adults with smartphones are randomly​ selected, 43% use them in meetings or classes. If 14 adult smartphone users are randomly​ selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes. The probability is?

Suppose repetitions are not allowed. Randomly pick up a three-digit number that is formed from the five digits: 1,2,3,4,5. What is the probability that this number exceeds 300?

The probability that an individual is left-handed is 12%. In a randomly selectedclass of 30 students, what is the probability of finding exactly 4 left-handedstudents?

Assume that when adults with smartphones are randomly​ selected, 56​% use them in meetings or classes. If 77 adult smartphone users are randomly​ selected, find the probability that exactly 33 of them use their smartphones in meetings or classes. The probability is?