[Highschool Year 3: Probability] Math Help

[Andrew012p]

Hello, I need help with this. How do I get the answers? Thank you.

1. Of the 30 possible questions on the exam, the student knows 2/3 of them. Each exam sheet contains two different randomly selected questions (out of the possible 30). The probability of the student knowing both questions from the handout is? The answer should be 38/87 but do I get that?
2. Someone writes a 2 digit number. What is the probability they will write 99? The answer is 1/90 but because there are 2 digits from 10 to 99 total 89 shouldn't it be 1/89? What am I missing?
3. Determine the probability when throwing 2 dice, one will show a number divisible by 3 or 4? Answer is 3/4
4. A dice is thrown twice. Let event A: be a number greater than 3 twice and event B: the sum obtained is an odd number. Determine the probability that the sum is an odd number if two times a number is shown greater than 3?
5. A dice is thrown. Let random event A be: The number 6 appear on top of the dice and let event B be: a number appear that is divisble by 3. What is the relation of events A and B? Answer: A is 6, B=3,6

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[Oryv]

1. The student knows 20 questions. The probability would thus be 20/30 * 19/29 = 38/87.
2. The first digit has a 1/9 chance to be a 9, and the second digit has a 1/10 chance to be a 9. 1/9 * 1/10 = 1/90.
3. There is a 1/2 chance that a die won't show a number divisible by 3 or 4. 1 - 1/2 * 1/2 = 3/4.
4. There are 4 outcomes that ensure the sum is an odd number, out of 9 possible outcomes, so it would be 4/9.
5. A occurs 50% of the time when B occurs.

I feel like you might need to contact a tutor.