Section 1
Introduction; definition of probability
Find the probability that a single throw of a dic will give a number less than $3 ;$ an even number; a $6 .$
Three coins are tossed; what is the probability that two are heads and one tails? That the first two are heads and the third tails? If at least two are heads, what is the probability that all are heads?
In a box there are 2 white, 3 black, and 4 red balls. If a ball is drawn at random, what is the probability that it is black? That it is not red?
A single card is drawn at random from a shuffled deck. What is the probability that it is red? That it is the ace of hearts? That it is either a three or a five? That it is either an ace or red or both?
Given a family of two children (assume boys and girls equally likely, that is, probability $\frac{1}{2}$ for each), what is the probability that both are boys? That at least one is a girl? Given that at least one is a girl, what is the probability that both are girls? Given that the first two are giris, what is the probability that an expected third child will be a boy?
A trick deck of cards is printed with the hearts and diamonds black, and the spades and clubs red. A card is chosen at random from this deck (after it is shuffled). Find the probability that it is either a red card or the queen of hearts. That it is either a red face card or a club. That it is either a red ace or a diamond.
A letter is selected at random from the alphabet. What is the probability that it is one of the letters in the word "probability?"' What is the probability that it occurs in the first half of the alphabet? What is the probability that it is a letter after $x$ ?
An integer $N$ is chosen at random with $1 \leq N \leq 100$. What is the probability that $N$ is divisible by 11? That $N>90$ ? That $N \leq 3$ ? That $N$ is a perfect square?
You are trying to find instrument $A$ in a laboratory. Unfortunately, someone has put both instruments $A$ and another kind (which we shall call $B$ ) away in identical unmarked boxes mixed at random on a shelf. You know that the laboratory has $3 \mathrm{~A} \mathrm{~s}$ and $7 \mathrm{~B}^{\prime} \mathrm{s}$. If you take down one box, what is the probability that you get an $A$ ? If it is a $B$ and you put it on the table and take down another box, what is the probability that you get an $A$ this time?
A shopping mall has four entrances, one on the North, one on the South, and two on the East. If you enter at random, shop, and then exit at random, what is the probability that you enter and exit on the same side of the mall?