To find the probability of answering all four questions correctly, we need to determine the probability of guessing each question correctly and then multiply those probabilities together.
For the true/false questions, since there are two options (true or false) for each question, the probability of guessing correctly for each true/false question is 1/2 or 0.5.
For the multiple-choice question with 4 possible answers, the probability of guessing correctly is 1 out of 4, which can be expressed as 1/4 or 0.25.
For the multiple-choice question with 5 possible answers, the probability of guessing correctly is 1 out of 5, which can be expressed as 1/5 or 0.2.
Now, we multiply these probabilities together to find the probability of answering all four questions correctly:
Probability = (Probability of true/false question 1) × (Probability of true/false question 2) × (Probability of multiple-choice question 1) × (Probability of multiple-choice question 2)
= (0.5) × (0.5) × (0.25) × (0.2)
= 0.0125 or 1.25%
Therefore, the chance that the student will answer all four questions correctly by random guessing is approximately 1.25%.