What notation do we use for finding the probability that the sum is 6 given that the first die is a 5? P(1st is 5 | sum is 6) P(1st is 5 and sum is 6) P(sum is 6) and P(1st is 5) P(sum is 6 | 1st is 5) P(the sum is 6 given that the first die is a 5) P(the sum is 6 and the first die is a 5) Which event is used to find the restricted space? the 1st die is a 5 sum of 6 and 1st is 5 sum of 6 given 1st is 5 the sum is 6 Which event is used to find the event space? the 1st die is a 5 the sum is 6 sum of 6 given 1st is 5 sum of 6 and 1st is 5 What is the probability that the sum is 6 given that the first die is a 5?  (Give answer as a decimal correct to three decimal places.)

Q: 4. A bag has 9 coins in total. There are three coins that have "heads" on both sides; four coins…

A: The bag has total 9 coins.

Q: A deck consists of playing cards that can have one of 12 suits and one of 6 ranks. A hand is a set…

A: It is required to find the number of possible four of a kind hands from the deck, and the…

Q: A bag contains a total 20 marbles; 8 blue, 7 red, and 5 white If 2 marbles are chosen without…

A: From the provided information, Total marbles a bag contains = 20 Blue marbles = 8 Red marbles = 7…

Q: If you throw a pair of regular standard die, what is the probability that you will get a sum of 6 OR…

A:

Q: In the cafeteria, there are 7 teachers, 48 girls, and 45 boys. What is the probability that a person…

A: We have given that, In a Cafeteria, there are 7 teachers, 48 girls and 45 boys. Total person in the…

Q: Find the probability of tossing and getting tails and a Coin then drawny a club card from 52 cards…

A: A coin is tossed and the deck of 52 cards are taken.

Q: If the probability that one student can solve a problem is 4/5 and that the probability of another…

A:

Q: Suppose we have a box that has 30 balls numbered 1 to 30. You draw three balls at random without…

A:

Q: Suppose you roll a fair die twice. Find the probability that the sum of the numbers is 4 Find the…

A: The sum is 4 for the outcomes=(1,3),(2,2),(3,1) And when a die is rolled then there are 6 outcomes…

Q: Example 9: On a library shelf, you can find 4 statistics books, 5 math books and 3 chemistry books.…

A: Introduction :-  Given that there are 4 statistics books, 5 math books, 3 chemistry books. Let ,  X1…

Q: A poker player has either good luck or bad luck each time she plays poker. She notices that if she…

A: Given data A poker player has either good luck or bad luck each time she plays poker. she notices…

Q: A party host gives two prizes to two different guests chosen at random. There are 10 men and 12…

A: given  data,A party host gives two prizes to two different guests chosen at random,there are 10- men…

Q: An experiment is rolling two dice. What is the probability that the first die is a 3 given that the…

A: An experiment of rolling two dice the outcome is,

Q: Solve the problems. 1 One out of every three boxes of cereal has a prize in it. To find the…

A: The multiples of 3 in the table are 3 and 6.  For 3 and 6 the total number of outcomes=(13+7)=20

Q: Suppose you roll a fair die twice. Find the probability that the sum of the numbers is 11 Find the…

A: When a die is rolled twice then there are total 6×6=36 outcomes.  Among those 36 outcomes (5,6) and…

Q: Suppose that two fair dice are rolled. find the probability that the number on the first dice is a 4…

A:

Q: Three balls are selected randomly from a bag containing 4 red balls and 7 blue ones. Find the…

A: From the provided information, Red balls = 4 Blue balls = 7 Total balls = 11

Q: There are 33 m&m's in a box ,Of which are 1o bive |l yellow, 12 red o You randomy select one a…

A: According to the provided information, there are a total of 33 m&m's. In which: 10 blue, 11…

Q: Suppose you are going to form a committee of students and faculty. You have 6 total students and 25…

A: We have given that Number of students = 6 Number of faculty = 25 Total people = 6 + 25 = 31 Number…

Q: The chips shown are placed in a bag and drawn at random, one by one, without replacement. What is…

A: Total chips=3+3+1+9=16 Yellow chips=3, White chips=3, Red chips=1, Blue chips=9

Q: 2 3. ne spinners above are spun and stopped ndomly. What is the probability that the fference of the…

A: Given Total number of possible outcomes 5x5=25

Q: The digits 2, 3, 4, 5, 6, and 7 are randomly arranged to form a three-digit number. (Digits are not…

A: Given digits is 2,3,4,5,6,7No.of digits = 6No. of digits number to be arranged = 3

Q: question 7 Box A contains 2 white and 4 Black balls. Another box B contains 3 white and 5 black…

A: Given,Box A:no.of white balls=2no.of black balls=4Total no.of balls=6Box B:no.of white balls=3no.of…

Q: In a parking lot there are only white cars, green cars, and red cars. If one car is selected at…

A: Givenl In a parking lot there are only white cars, green cars, and red cars. If one car is selected…

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.