Probabilistic topics in the Champions League lottery

Topic 1 (c)

Because the value range of y is 0, not [0, 1].

Theme 2 (c)

The service time x before damage is exponentially distributed.

Topic 3 (a)

The first 9 times succeeded 3 times, and the first 10 time succeeded.

The probability of success three times in the first nine times: c (9 9,3) p 3 (1-p) 6.

Multiply by 10 success probability p.

Question 4 (a)

Because if the two are opposite, then: P(A|B) = 0, P(A'|B') = 0.

Question 5 (b)

The title is printed wrong. The colors of the two balls given are red and white, but yellow is sought.

What I want is a red ball.

This can be calculated by the full probability formula, or it can be directly obtained by the lottery principle.