Answer the word problems carefully.
A. Binomial Distribution (5pts each)
1. A multiple choice test contains 10 questions with answers a,b, and c. Only one of this represents the correct answer. Find the probability that the student will answer exactly 4 correct answers if he/she makes guesses on all 10 questions.
2. 30% of students are enrolled in a statistics class according to a certain survey on University X. 20 students are chosen at random, find the probability that there are exactly 8 students out of 20 students who are taking algebra.
B. Cumulative Binomial Distribution (10 pts)
1. An unbiased coin is tossed 6 times, what is the probability that you will get 4 heads at most?