Answer:
(a) 2048
(b) [tex]\frac{1}{2048}[/tex].
Step-by-step explanation:
(a)
Total number of questions = 11
Each equation has two possible answers (either true or false).
We need to find the total number of ways in which the test can be completed.
[tex]\text{Total number of ways}=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2[/tex]
[tex]\text{Total number of ways}=2^{11}[/tex]
[tex]\text{Total number of ways}=2048[/tex]
Therefore the total possible ways to complete the test is 2048.
(b)
We need to find the probability that a test is randomly answered perfectly.
Total Favorable outcomes = 1
Total possible ways = 2048
[tex]Probability=\frac{\text{Total Favorable outcomes}}{\text{Total possible ways}}[/tex]
[tex]Probability=\frac{1}{2048}[/tex]
Therefore the probability that a test is randomly answered perfectly is [tex]\frac{1}{2048}[/tex].
