Suppose you roll a fair die twice. Find the probability that the sum of the numbers is 4 Find the probability that the sum of the numbers is 4 given the first dice rolled is a 3

Q: You roll a standard die 3 times. What is the probability you roll a 6 on the first roll, an even…

A: If standard die is rolled than the possible outcomes ares=(1,2,3,4,5,6)No.of even numbers=3…

Q: Find the probability of the following. 1. A box contains 6 red balls, two green balls, 1 blue ball,…

A: Given: Total number of balls=10Number of red balls=6Number of white balls=1 The probability of…

Q: You roll a fair six-sided die twice. Find the probability of rolling a 1 the first time and a number…

A:

Q: If pair of dice is thrown . Find the probability that a,scoring 3 followed by 4 b,the sum of the top…

A:

Q: When rolling a number cube 800 times what is the probability that a 2 or 5 would be rolled

A: Total Number of faces = 6 P(2) =1/6 P(5)= 1/6 Now, Probability of 2 or 5 is: P(2∪5)=P(2)+P(5)-P(2∩5)…

Q: We roll a pair of dice three times. Find the probability that a total of five is rolled each time.

A: If we roll a pair of dice one time then the possible outcomes of gettingsum as 5…

Q: In a carnival game, you roll a number cube and flip a coin. The sides of the die contain the numbers…

A: Introduction: It is required to find the probability of winning the game by scoring 10 or more…

Q: There are 7 male students and 22 female students in a class. If you choose 2 students at random,…

A: We have given that 2 Number of Male students =7 Number of female students =22 Total possible cases =…

Q: A pair of dice are tossed twice. Find the probability that the first roll is a total of at least 12…

A: roll pair of dice twice.  roll dice : {1,2,3,4,5,6} for rolling pair of dice : total outcomes = 36

Q: Flip a dime and a penny at the same time. Find the probability of the event that two faces are the…

A: Given: A dime and a penny at the same time. Faces of both dime and a penny can be named as Heads(H)…

Q: Suppose you have 10 tennis balls and you randomly pick some number of them. What is the probability…

A: Given the event that there are 10 tennis balls and one randomly pick some number of them.

Q: Toss a balanced dice once. Find the probability to get a 6. If you are given that even numbers are…

A:

Q: You roll a fair six-sided die twice. Find the probability of rolling a 1 the first time and a number…

A: We can roll 1 in only 1 way.For a die there are 6 possible outcomes.So, the probability of rolling a…

Q: If you know that the probability Ali scores a goal is 0.78, then the probability that his fifth goal…

A: Probability ( 5th goal on his 8th shot is)=.00307

Q: A person randomly rolls two dice repeatedly. Find the probability that the first time the sum is…

A: We have to find given probability...

Q: Roll a fair die once and then select a card from a standard 52 card deck. Calculate The probability…

A: From the given information we find the given probability.

Q: A pair of fair dice are rolled. Find the probability that the sum is equal to 5. Find the…

A: you roll a fair die twice. then sample space(S);…

Q: Two dice are rolled. Find the probability that the sum of the dice is not more than 6

A: If we roll two dice then there are total 36 outcomes. n=36 we can show the outcomes with the help of…

Q: Ian rolls the two dice and will win the game if the sum of the numbers of the two dice is 8. What is…

A: Two dice are rolled, outcome of this event is: Ω= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),…

Q: Say you roll two dice. Find the probability c rolling a number greater than 2 on the first, and then…

A:

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: Roll a pair of dice 10 times. Determine the probability of having exactly

A: Given that the pair of dice is rolled 10 times. When rolling pair of dice, the possible outcomes for…

Q: A pair of dice is rolled. Find the probability that the sum of the two dice is 10 or higher

A: A pair of dice is rolled.

Q: A box contains 3 red balls and 4 blue balls. If two balls are drawn in succession, what is the…

A: Given that  Total balls=3+4=7 Red balls=3 Blue balls=4 Find  P(red and other blue)

Q: A pair of dice are tossed twice.Find the probability that the first roll is a total of at least 11…

A: The objective of this question is to find the probability of two independent events happening. The…

Q: rolled and the numbers are noted. Find the probability that the sum of the numbers is 4 o

A: Two dice are rolled. The numbers are noted.

Q: You have a 30-sided dice. Your friend Hugo has three favorite numbers: 5, 3, and 10. What is the…

A: Given You have a 30-sided dice. Your friend Hugo has three favorite numbers: 5, 3, and 10.

Q: QUESTION 7 The fill weight of a certain brand of adult cereal is normally distributed with a mean of…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If you roll n fair 6-sided dice, find the probability that the sum of the numbers on top is n+5.

A:

Q: A pair of dice are tossed twice. Find the probability that both rolls give at most a sum of 6.

A: We have given that,  A pair of dice are tossed twice then the sample space (S) is,  S = {(1,1),…

Q: Two dice are thrown together.What is the probability that the sum of the number on the two faces is…

A:

Q: You roll a die five times. What is the probability that you will see a string of three or more…

A: Given data: *The die is rolled 5 times, n=5. The probability of getting one (success) when a one die…

Q: If you roll 6 six-sided dice, find the probability that the sum of the dice is greater than 7.

A: A six-sided die is rolled 6 times. The objective is to find the probability that the sum of the dice…

Q: ou roll a fair six sided die twice. Find the probability of rolling a 1 the first time and a number…

A: n(S) = 36 Let A = rolling a 1 and then greater than 5 = {(1,6)} n(A) = 1

Q: Find the probability of rolling two dice that add up to 3 or 7. (leave your answer as a reduced…

A: Find the probability of rolling two dice that add up to 3 or 7.

Q: If 25 dice are rolled, find the probability the three 6s are seen.

A:

Q: Caleb rolls two regular six sided dice determine the odds against him rolling an odd or a sum of 4

A: Given that Caleb rolls two regular six sided dice we have to find the odds against him rolling an…

Q: You roll a 6-sided die then toss a coin. Find the probability of rolling a number greater than 1 and…

A: n(S) = 12 Let A = rolling a number greater than 1 and the coin landing on tails Then, n(A) = 5

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.