Exam 7: A: Discrete Probability

you flip a biased coin, where p(heads) = 3/4 and p(tails) = 1/4, ten times. - $\text { Find } p \text { (exactly } 9 \text { heads). }$

you have 40 different books (20 math books, 15 history books, and 5 geography books). -You pick one book at random. What is the probability that the book is not a geography book?

You flip a coin. If it lands heads, you lose 1 point. If it lands tails, you flip the coin again, and lose 1 point

What is the probability that a card chosen from an ordinary deck of 52 cards is an ace?

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors. -You pick two students at random, one at a time. What is the probability that the second student is a freshman, given that the first is a freshman?

an experiment consists of picking at random a bit string of length five. Consider the following events: E1: the bit string chosen begins with 1; E2: the bit string chosen ends with 1; E3: the bit string chosen has exactly three 1's. -Find $p \left( E _ { 3 } \mid E _ { 2 } \right)$ .

Each of 26 cards has a different letter of the alphabet on it. You pick one card at random. A vowel is worth 3 points and a consonant is worth 0 points. Let X = the value of the card picked. Find E(X), V (X), and the standard deviation of X .

you have 40 different books (20 math books, 15 history books, and 5 geography books). -You pick one book at random. What is the probability that the book is a history book?

an experiment consists of picking at random a bit string of length five. Consider the following events: E1: the bit string chosen begins with 1; E2: the bit string chosen ends with 1; E3: the bit string chosen has exactly three 1's. - $\text { Find } p \left( E _ { 1 } \mid E _ { 3 } \right) \text {. }$

What is the probability that a randomly selected integer chosen from the first 100 positive integers is odd?

A red and a green die are rolled. What is the probability of getting a sum of six, given that the number on the green die is odd?

In a certain lottery game, you choose a set of six numbers out of 54 numbers. Find the probability that none of your numbers match the six winning numbers.

you pick a bit string from the set of all bit strings of length ten. -What is the probability that the bit string has exactly two 1's, given that the string begins with a 1?

What is the probability that a fair coin lands Heads 6 times in a row?

You have seven cards, numbered 3 through 9, and you pick one at random. If you pick a card with a prime number, you get 1 point; if you pick a card with a composite number, you lose 1 point. Find the expected value of the number of points you get.

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors. -You pick two students at random, one at a time. What is the probability that both are freshmen?

you flip a biased coin, where p(heads) = 3/4 and p(tails) = 1/4, ten times. -Find p(exactly 7 heads).

In a certain lottery game, three distinct numbers between 10 and 25 (inclusive) are chosen as the winning numbers. What is the probability that the winning numbers are all composite numbers.

you have 40 different books (20 math books, 15 history books, and 5 geography books). -You pick two books at random, one at a time. What is the probability that both books are history books?

Find and correct the error in the solution to the following problem: Problem: You flip two coins and want to find the probability that both coins show heads. Solution: There are three possible outcomes: 2 heads, 2 tails, or 1 head and 1 tail. Since a "success" is one of these three outcomes, $p ( \text { both heads } ) = 1 / 3$