Amultiple choice test contains 10 questions, each with 3 possible answers (of which only one is correct). if a student answers each question by rolling a die and choosing the first answer if the die shows 1 or 2, the second answer if the die shows 3 or 4, or the third answer if the die shows 5 or 6, what is the probability that the student will get exactly 6 correct answers? more than 6 correct answers?

1. The probability that the student will get exactly 6 correct answers is .

2. The probability that the student will get more than 6 correct answers is .

Step-by-step explanation:

From the given information it is clear that

The total number of equations (n) = 10

The probability of selecting the correct answer (p)=

The probability of selecting the incorrect answer (q)=

According to the binomial distribution, the probability of selecting r items from n items is

where, p is probability of success and q is the probability of failure.

The probability that the student will get exactly 6 correct answers is

Therefore the probability that the student will get exactly 6 correct answers is .

The probability that the student will get more than 6 correct answers is

Therefore the probability that the student will get more than 6 correct answers is .