wo six-faced unbiased dice are thrown together. Calculate the probability that (a) the sum of two numbers is 8. (b) the difference of two numbers is 5. (c) the sum of two numbers is 8 or the difference of two numbers i

Q: Jack and Tim play a rock-paper-scissors game. They play a total of 3 independent games, the one who…

A: Given the games played independently Therefore, Winning of game is equally likely Probability Jack…

Q: We roll Two dice and report the sum of the spots on the up faces.  What is the probability of…

A: From the given information, two dice are rolled. The total sample space is,

Q: n order to qualify for the next round, soccer team has to get at least 4 points in the next 2 games.…

A: The requirement of points for qualify in the next round is 4 points. Points on victory is 3 Points…

Q: Suppose you roll two six sided dice and add the results together. What are the odds that you will…

A: Suppose you roll two six sided dice and add the results together   The sample space would be :…

Q: I roll 12 fair and 6 sided dices. I obtain a sum. How do I calculate the probability of the sum…

A: 12 fair dice of 6 sided faces Total outcomes =  6^12 = 2176782336 Probability = favorable outcomes…

Q: When I drive from my apartment to UCSD, I want to choose 2 out of 5 songs from Olivia Rodrigo's new…

A: From the given information,out of 5 songs, 2 songs must be chosenThe order of songs mattersVampire…

Q: You are ordering a hamburger and can get up to 7 toppings, but each topping can only be used once.…

A: 4 toppings can be chosen from 7 by 7C4 Ways 7C4 =

Q: Roll two fair dice at a time.  What is probability of rolling sum of 7?

A: The sample space when rolling to fair dice are: 62=36 And the sample space with total sum seven:…

Q: A bag contains 2 red marbles and 5 white marbles. What is the probability of drawing two red marbles…

A: What is the probability of drawing two red marbles at random if the first marble drawn is not…

Q: We roll a dice and flip a coin.

A:

Q: Todd and Tiff both train pets. Todd trains 30% of pets and Tiff trains 70% of pets. Todd’s pets are…

A: Given that P(Todd trains)=0.30 P(Tiff trains)=0.70 P(female| Todd) =0.55 P(female| Tiff) =0.65

Q: A coin is tossed 12 times. Y= Number of Tails .Find the probability of getting (i) 3 tails (ii) at…

A:

Q: The probability of A is 0.60, the probability of B is 0.40, and the probability of either is 0.76.…

A: Given: P(A)=0.6 P(B)=0.4 P(A or B)=0.76 The objective is to find the P(A and B)

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: Three people are selected for a committee from 7 Democrats and 5 Republicans. What is the…

A: Given information: Frequency of Democrats, d = 7 Frequency of Republicans, r = 5 A committee of x =…

Q: In order to qualify for the next round, soccer team has to get at least 4 point in next 2 games.…

A: Given that to qualify the soccer team has to get at least 4 points in the next 2 games. So there can…

Q: Over a weekend, Ivan counted the number of single scoop ice creams ordered at his store. He tracked…

A: Probability of an event is the chances of occurrence of the event and it can take values from 0 to…

Q: In the toss of three dice, what is the probability of obtaining 2 twos and 1 four? Please answer…

A: Answer:- Given, three dice are tossed,                what is the probability of obtaining 2 twos…

Q: Q1- A box contains four chocobars and four ice creams. Tom eats 3 of them one after another. What is…

A: Solution is given below

Q: Find the probability of getting a sum of 6 on two dice if the first die is already shows a 3.

A: Probability : Probability could be a discipline of arithmetic involved with numerical explanations…

Q: Steve has 12 biscuits in a tin. There are 5 digestive and 7 chocolate biscuits. Steve takes two…

A: Given that, Total number of biscuits = 12 5 digestive biscuits and 7 chocolate biscuits We to find…

Q: At Shakey's Pizza, 45% of customers order pizzas with either sausage or pepperoni. If 31% get only…

A:

Q: a small restaurant offers a dinner menu of 4 salads 6 entrees and 2 desserts. what is the…

A: Given Data: The number of salads in the restaurant is: s=4 The number of entress in the restaurant…

Q: Brad has to select 5 students from a class of 43 girls and 21 boys. What is the probability that…

A: GivenNo.of girls in a class = 43No.of boys in a class = 21Total no. of boys = 64

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: You have 3 tops: green, white, and yellow. You have 2 pairs of pants: blue and black. You have 2…

A: Given data: The numbers tops are T=3. The numbers pants are P=2. The numbers of shoes are S=2.

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: You randomly select one card from a​ 52-card deck. Find the probability of selecting the king of…

A: It is known that Number of cards in a deck = 52 Number of king of diamonds = 1 Number of two of…

Q: A game is played by rolling the two dice, three times (toss the two dice three times). What is the…

A: It is given that there are two dice that are thrown three times. Consider that D1 and D2 are defined…

Q: find the probability that the sum of the 2 dice is an even number or a number less than 5

A: When two dice are thrown then these following cases occur  sum Outcomes Number of outcomes…

Q: Determine the probability that the rolled dice will result to a multiple of 3 or a square number.

A: It is known that, the outcomes of rolling a die are 1, 2, 3, 4, 5, and 6.

Q: The probability of A is 0.60, the probability of B is 0.45, and the probability of either is 0.80.…

A: Given:PA=0.6PB=0.45PA∪B=0.8

Q: What is probability of getting a total of 6 or 10 when a pair of dice is tossed?

A: I solved exactly first question because of bartleby policy if you want more please uplode…

Q: Two dice are thrown. Determine the probability of getting 4 points.

A:

Q: A pair of dice is rolled. What are the odds of rolling a sum of 4 or a sum of 7? The odds of rolling…

A:

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

A:

Q: Nancy is playing cards. What is probability of pulling a diamond or 4 of clubs?

A: nancy is playing cards. p(pulling diamond or 4 of clubs) = ? there are 13 cards of diamonds and 1…

Q: in a break room there are 3 bags of pretzels 2 bags of doritos and 4 bags of popcorn .find the…

A: Total number of bags = 9 (i.e. 3+2+4) Number of pretzels bags = 3 Number of Doritos  bags= 2 Number…

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: What is the probability of getting at least one 4 when you throw 2 dice?

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: Whitney wants to practice shooting for basketball.  Her mom will give her $20 if she makes 3 free…

A: If each trial has only two possible outcomes, that is, success and failure, the probabilities of…

Q: We throw three independent fair dice. Find the probability that the sum of the outcomes is equal to…

A: When die is rolled, there would be 6 possible outcomes1,2,3,4,5,6. For drawing three independent…

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.