3 students apply to a PhD program. The program rejects 25%…
3 students apply to a PhD program. The program rejects 25% of all applicants. Students are accepted and rejected independently of each other. Let the random variable X represent the number of the 3 students who get rejected into the PhD Program. What is the probability that 1 student is rejected to the program if it is known that at fewer than 2 students will be rejected? (round your answer to 4 decimal places) (Hint: Binomial distribution with P=25% and n=3, and conditional probability)