Question 1

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?

Accepted Answer

15/40

Question 2

What is the probability that a randomly selected day of the year (366 days) is in May?

Accepted Answer

31/366

Question 3

In a certain lottery game, you choose a set of four diﬀerent integers between 1 and 50, inclusive, and a ﬁfth integer between 1 and 20, inclusive, which may be the same as one of the other four. (a) What is the probability you win the jackpot by matching all ﬁve numbers drawn? (b) What is the probability that you match three of the ﬁrst four numbers, but not the ﬁfth?

Accepted Answer

(a) $1 / \left( \left( \begin{array} { c } 50 \ 4 \end{array} \right) \cdot 20 \right)$
(b) $\left( \left( \begin{array} { l } 4 \ 3 \end{array} \right) \cdot 46 \cdot 19 \right) / \left( \left( \begin{array} { c } 50 \ 4 \end{array} \right) \cdot 20 \right)$

Question 4

Three coins are tossed. (a) List the elements in the sample space. (b) Find the probability that exactly two heads show.

Accepted Answer

The answer of Three coins are tossed. (a) List the...

Question 5

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.

Accepted Answer

The answer of In a certain lottery game, three distinct...

Question 6

What is the probability that the sum of the numbers on two dice is even when they are rolled?

Accepted Answer

The answer of What is the probability that the sum...

Question 7

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

Accepted Answer

The answer of What is the probability that a card...

Question 8

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?

Accepted Answer

The answer of you have 40 diﬀerent books (20 math...

Question 9

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.

Accepted Answer

The answer of In a certain lottery game, you choose...

Question 10

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

Accepted Answer

The answer of What is the probability that a fair...

Question 11

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

Accepted Answer

The answer of What is the probability that a randomly...

Question 12

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors.
-You pick one student at random. What is the probability that the student is not a junior?

Accepted Answer

The answer of suppose you have a class with 30...

Question 13

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?

Accepted Answer

The answer of you have 40 diﬀerent books (20 math...

Question 14

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?

Accepted Answer

The answer of suppose you have a class with 30...

Question 15

Prove or disprove: $p ( E \cup F ) = p ( E ) + p ( F ) \text { for all events } E \text { and } F$

Accepted Answer

Choose one card at random from a deck of 52 cards. Let E = choose a diamond, F = choose a king. $\text { Then } p ( E \cup F ) = 16 / 52 \text { while } p ( E ) + p ( F ) = 17 / 52 \text {. }$

Question 16

What is the probability that a fair coin lands Heads 4 times out of 5 ﬂips?

Accepted Answer

The answer of What is the probability that a fair...

Question 17

Let A be the set of all strings of decimal digits of length 5. For example, 00312 and 19483 are two strings in A. You pick a string from A at random. What is the probability that (a) the string begins with 7575. (b) the string has no 4 in it.

Accepted Answer

The answer of Let A be the set of all...

Question 18

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, $p ( \text { both heads } ) = 1 / 3$

Accepted Answer

The answer of Find and correct the error in the...

Question 19

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?

Accepted Answer

The answer of suppose you have a class with 30...

Question 20

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 the two books are from diﬀerent disciplines?

Accepted Answer

The answer of you have 40 diﬀerent books (20 math...

Quiz 7: A: Discrete Probability

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?

What is the probability that a randomly selected day of the year (366 days) is in May?

Three coins are tossed. (a) List the elements in the sample space. (b) Find the probability that exactly two heads show.

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.

What is the probability that the sum of the numbers on two dice is even when they are rolled?

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

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?

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.

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

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

suppose you have a class with 30 students-10 freshmen, 12 sophomores, and 8 juniors. -You pick one student at random. What is the probability that the student is not a junior?

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?

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?

Prove or disprove: p(E∪F)=p(E)+p(F) for all events E and Fp ( E \cup F ) = p ( E ) + p ( F ) \text { for all events } E \text { and } Fp(E∪F)=p(E)+p(F) for all events E and F

What is the probability that a fair coin lands Heads 4 times out of 5 ﬂips?

Let A be the set of all strings of decimal digits of length 5. For example, 00312 and 19483 are two strings in A. You pick a string from A at random. What is the probability that (a) the string begins with 7575. (b) the string has no 4 in it.

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 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 the two books are from diﬀerent disciplines?

Prove or disprove: $p ( E \cup F ) = p ( E ) + p ( F ) \text { for all events } E \text { and } F$