Answer :

Final answer:

The detailed answer explains how to calculate the probability of passing a true-false test with at least a 70% score by considering all possible outcomes and favorable combinations.


Explanation:

Probability Calculation:

To calculate the probability of passing with at least 70%, we need to consider the different possibilities. Out of the 10 questions, if the student randomly guesses, there are 2^10 = 1024 possible outcomes. To pass with at least 70%, the student needs to get 7, 8, 9, or 10 questions correct. The combinations for each are:

  • 7 correct: 10C7 = 120
  • 8 correct: 10C8 = 45
  • 9 correct: 10C9 = 10
  • 10 correct: 10C10 = 1
The total favorable outcomes are the sum of these combinations. Divide the total favorable outcomes by the total possible outcomes to get the probability of passing with at least 70%.

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