11 A test consists of 6 multiple choice questions with three

11. A test consists of 6 multiple choice questions with three choices for each question. As an experiment, you \"guess\" on each and every question without even reading the question. What is the probability of getting at least 4 questions correct on this test? The following equation will assist you in solving this problem. (k)p* (1 - p)-k. (6 points) 12. Given the following geometric sequence: 3.Determine the formula for the … 27\' Then find the 10th term of the sequence. sequence in the form anar-1; recall r (6 points) an-1

Solution

6 questions....

Atleast 4 questions right...

P(4 right) + P(5 right) + P(6 right)

6C4 * (1/3)^4 * (2/3)^2 + 6C5 * (1/3)^5 * (2/3)^1 + 6C6 * (1/3)^6

= 73/729 ----> ANS

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r = (2/9) / (1/3)
r = 2/9 * 3
r = 2/3

Now, an = a1 * r^(n - 1)

= 1/3 * (2/3)^(n - 1)

10th term :
1/3 * (2/3)^9

= 2^9 / 3^10 ---> ANS