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A Ratio of Uniforms

$X$ and $Y$ are independently and uniformly distributed on $[0,1]$ . What is $P(1 < X/Y < 3)$ ?

Assuming $365$ equally likely birthdays, what is the smallest group size for which a shared birthday is more likely than not?

A fair coin is tossed until either three consecutive heads or three consecutive tails appear. What is the probability heads wins?

From 6 women and 5 men, how many 4-person committees contain exactly 2 women?

Four letters are placed randomly into four addressed envelopes. What is the probability no letter reaches its correct recipient?

A standard 52-card deck is shuffled. What is the probability all four aces are consecutive?

A fair die is rolled until the first six appears. What is the expected number of rolls?

How many rolls of a fair six-sided die are expected until every face has appeared?

If $X_1,X_2,X_3$ are independent $\operatorname{Uniform}[0,1]$ variables, what is $\mathbb{E}[\max(X_1,X_2,X_3)]$ ?

A population has variance $16$ . For a random sample of $64$ independent observations, what is the standard error of the sample mean?

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