Questions asked
You want to invent a gambling game in which a person rolls two dice and is paid some money if the sum is 6, but otherwise he loses his money (a bet). How much should you pay him for winning a $2 bet if you want this to be a fair game, that is, to have expected value 0?
Suppose we pick 4 students at random from a class with 15 boys and 20 girls. Let X be the number of boys selected and Y be the number of girls selected. Find E(X − Y).
You draw 6 cards from a deck of 52 cards without repetition. Let X be the number of selected aces. Find the mean of X.
You draw cards one at a time from a deck of 52 cards with repetition (you return the selected card to the deck each time) until an ace appears. Let X be the number of trials. Find the mean of X.
You draw 4 cards one at a time from a deck of 52 cards with repetition (you return the selected card to the deck each time). Let X be the number of selected aces. Find the mean of X.
In a popular gamble, three dice are rolled. For a $1 bet you win $1 for each six that appears (plus your dollar back). If no six appears you lose your dollar. What is your expected value?
A random variable has PMF (probability mass function) P(X = x) = x/30 for x = 2, 4, 6, 8, 10 and 0 otherwise. Is it a valid PMF? Is so, find the mean of X.
You draw 6 cards one at a time from a deck of 52 cards with repetition (you return the selected card to the deck each time). Describe the distribution of the number of selected aces. Give the name of the distribution.
You draw cards one at a time from a deck of 52 cards with repetition (you return the selected card to the deck each time) until an ace appears. Describe the distribution of the number of selected cards including the last one (an ace). Give the name of the distribution.
Jason Horton
Numerade educator
There are 10 000 lottery tickets marked 0000 to 9999. One of these is selected at random. What is the probability that the number on it contains 84 (consecutive, in that order) at least once?