Suppose a particle moves along tje x-axis beginning at 0. It moves one integer step to the left or right with equal probability. What is the probability function of its position after four steps?

A professor of management has heard that eleven students in his class of 37 have landed an internship for the summer. Suppose he runs into two of his students in the corridor.  a. Find the probability that neither of these students has landed an internship. (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) b. Find the probability that both of these students have landed an internship.

A place kicker in pro foot ball has a 77% probability of making a field goal  over 40 yd and each attempted field goal is independent if the kicker made his 1st two but missed his 3rd attempt and is now trying for his 4th field goal of the game to win in overtime what is the probability that his team will win the game

A student in this class is writing two midterms in math this week. The probability that she will pass MAT 2371 is 0.7, and the probability that she will pass MAT 2125 is 0.7. If the result on the two exams are independent, what is the probability that she will fail at least one the two exams? 0.56 0.44 0.54 0.46 0.51