Final answer:
The equation 2/10 = 20% = 0.2 is true. For the probability of passing a true-false quiz by guessing, we'd need to calculate the cumulative probability of getting at least 7 out of 10 answers correct, which involves the binomial probability formula.
Step-by-step explanation:
The statement 2/10 = 20% = 0.2 is indeed true. Each representation is a different way to express the same proportional or fractional value. In mathematics, percentages, decimals, and fractions are interconnected, and converting between them is a fundamental skill.
As for the probability question, if a student randomly guesses on a 10-question true-false quiz, they need to get at least 7 out of 10 questions right to pass with a grade of at least 70%. The probability of guessing each question correctly is 1/2 since there are only two possible answers. To calculate the probability of getting exactly 7, 8, 9, or 10 questions correct, we use the binomial probability formula. However, this calculation can become complex and often requires the use of a calculator or knowledge of binomial probability tables.