IMathAS-libretexts

Identify the problem involving a binomial experiment.

The local weather forecaster predicts that there is a 30% chance of rain on each day next week. Assuming his prediction is accurate, what is the probability it will rain on at least 2 of the days next week?
Carlos plays soccer and has a 25% chance of scoring a goal on one of his shots. However, Carlos scores in streaks, so the probability of him scoring a goal on the shot immediately following a score is 50%. He takes 10 shots. What is the probability he scores on at least 3 of them? Of the 10 shots, what is the expected number of goals Carlos will score?
Cecelia has 16 library books at home, 5 of which are due today. As she is in a rush to get out of the house, she doesn't have time to examine the books to find the 5 that are due (and can't carry all 16). Instead, she randomly grabs 6 of them in hopes of getting at least 2 of the ones that are due. What is the probability she will actually grab at least 2 of the ones that are due?
Dr. Brin has graded 40 exams, 33 of which received passing grades. Suppose he reviews a random selection of 10 exams. How many should he expect to have passing grades? How many should he expect to have failing grades? What is the probability that at least 5 of the exams have failing grades? What is the probability that 7 of the exams have passing grades?