According to the "january theory," if the stock market is up for the month of january, it will be up for the year. if it is down in january, it will be down for the year. according to an article in the wall street journal, this theory held for 22 out of the last 34 years. suppose there is no truth to this theory; that is, the probability it is either up or down is 0.5. what is the probability this could occur by chance? (round your answer to 6 decimal places.)

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?

An engineer scale model shows a building that is 3 inches tall. if the scale is 1 inch = 600 feet, how tall is the actual building?

Two sides of a right triangle measure 2 units and 4 units. what is the area of the square that shares a side with the third side of the triangle?