Question

A student is appearing for a class quiz without preparing. There are 10 True/False questions all with only one correct choice and each carry 1 point. Being unprepared, the student decided to answer all questions randomly. What is the probability that he/she will score at least 5 points in the test?

Answer 1

The probability that the student will score at least 5 points in the test is 0.623.

Step-by-step explanation:

To find the probability that the student will score at least 5 points in the test, we will consider all possible ways the student can score 5, 6, 7, 8, 9, or 10 points. Let's calculate the probability for each score:

• Score 5: There are 10 ways to randomly answer 5 questions correctly (choosing 5 true answers and 5 false answers), so the probability is (10 choose 5) / (2^10) = 252 / 1024.
• Score 6: There are 10 ways to randomly answer 6 questions correctly, so the probability is (10 choose 6) / (2^10) = 210 / 1024.
• Score 7: There are 10 ways to randomly answer 7 questions correctly, so the probability is (10 choose 7) / (2^10) = 120 / 1024.
• Score 8: There are 10 ways to randomly answer 8 questions correctly, so the probability is (10 choose 8) / (2^10) = 45 / 1024.
• Score 9: There are 10 ways to randomly answer 9 questions correctly, so the probability is (10 choose 9) / (2^10) = 10 / 1024.
• Score 10: There is 1 way to randomly answer all 10 questions correctly, so the probability is (10 choose 10) / (2^10) = 1 / 1024.

To find the total probability of scoring at least 5 points, we sum up all the probabilities: (252 + 210 + 120 + 45 + 10 + 1) / 1024 = 638 / 1024 = 0.623.